import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf
import statsmodels.api as sm2
from sklearn.linear_model import LinearRegression
from sklearn import metrics
from sklearn.model_selection import train_test_split
from statsmodels.graphics.gofplots import qqplot_2samples, qqplot
import seaborn as sns
import statistics
%matplotlib inline

---

Table of Contents

Section 1 – Objectives of Your Project

Section 2 – Data Exploration

• Section 2.1. Types of Data
• Section 2.2. Completeness of Data
• Section 2.3. Does the Data Meet the Assumptions for Regression?
• Section 2.4. Data Exploration - Conclusion Summary

Section 3 – Correlation Analysis

• Section 3.1. Correlation Analysis of Period 1 - before 1920
• Section 3.2. Correlation Analysis of Period 2 - 1920 to 1959
• Section 3.3. Correlation Analysis of Period 3 - 1960 to 1989
• Section 3.4. Correlation Analysis of Period 4 - 1990 to 2010
• Section 3.5. Summary - Style of Play by Period

Section 4 – Linear Regression Models

• Section 4.1. Linear Regression Model for Period 4
• Section 4.2. Evaluation of Regression Model for Period 4

Section 5 - Model Validation

• Section 5.1. Helper Functions to Try New Models
• Section 5.2. Testing the Error of Predictions - Actual Wins vs. Predicted Wins
• Section 6 - Predictions
• Section 7 - Conclusions

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Section 1 – Objectives of Your Project

The project objective is to find the style of play of each team in different periods and how it affects the game win

Who needs the answers:

• Fans of the game

• Coaching staff and players to analyze competitors' strategy and make their own strategy

• Sports writers that need material for their writings

How do we do it?

• First, we explore the data to understand and determine its level of completeness
• Then, we do preliminary analysis across the entire data set to check the normality of the variable data and relationships between each independent variable and depedent variable by using scatterplots/scatter matrix, histogram plots, qqplots, and correlations
• Conduct simple linear regressions for each Independent variable and dependent variable pair by
• Next, we choose the candidate variables for the model based on the correlations and then we use the non-redundant independent variables in the analysis to find the best fitting model.
• We use train test slit to build and validate the model. We will slit the data set into 2: training data and test data. Training data will be used build the model, and test data will be used to validate it. To find best fit model, we will use Ordinary Least Squares regression (OLS) technique
• After fitting the model, we will interpret the statistical outputs uch as the coefficients, p-values (t-tests), R-squared, Adjusted R-squared, F-statistic and Prob (F-statistic), and RSME to check its significance.
• Our suggestion for thresholds of:

Level of significance: 95% (alpha is 5%)

RMSE: because of nature of the dependent variable, RMSE does not need to be too accurate (less than 1). We are suggesting the acceptable range for RMSE is +/ 5 games won. Or Scatter Index (normalized measure of error) is less than 5%

• Lastly, we predict the games won in a different time period by using actual independent variables in that period and the best fit model to calculate the y prediction, and compare the predicted y (predicted game wons) to the actual games won in that time period. By doing this, we will know the expected accuracy of the prediction (how good the model is in predict games won). This will be done

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Section 1 – Objectives of Your Project
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---

Section 2 – Data Exploration

Section 2.1. Types of Data

Read the data set

df=pd.read_csv('baseball_teams.csv',header=0)
df.head(10)

	Year	League	Team	Franchise	Division	Final_Standing	Games_Played	Unnamed: 7	Games_Won	Games_Lost	...	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name	Home_Ball_Park	Attendance
0	1871	NaN	BS1	BNA	NaN	3	31	NaN	20	10	...	367	2	42	23	225	NaN	0.83	Boston Red Stockings	South End Grounds I	NaN
1	1871	NaN	CH1	CNA	NaN	2	28	NaN	19	9	...	308	6	28	22	218	NaN	0.82	Chicago White Stockings	Union Base-Ball Grounds	NaN
2	1871	NaN	CL1	CFC	NaN	8	29	NaN	10	19	...	346	13	53	34	223	NaN	0.81	Cleveland Forest Citys	National Association Grounds	NaN
3	1871	NaN	FW1	KEK	NaN	7	19	NaN	7	12	...	261	5	21	17	163	NaN	0.80	Fort Wayne Kekiongas	Hamilton Field	NaN
4	1871	NaN	NY2	NNA	NaN	5	33	NaN	16	17	...	373	7	42	22	227	NaN	0.83	New York Mutuals	Union Grounds (Brooklyn)	NaN
5	1871	NaN	PH1	PNA	NaN	1	28	NaN	21	7	...	329	3	53	16	194	NaN	0.84	Philadelphia Athletics	Jefferson Street Grounds	NaN
6	1871	NaN	RC1	ROK	NaN	9	25	NaN	4	21	...	315	3	34	16	220	NaN	0.82	Rockford Forest Citys	Agricultural Society Fair Grounds	NaN
7	1871	NaN	TRO	TRO	NaN	6	29	NaN	13	15	...	431	4	75	12	198	NaN	0.84	Troy Haymakers	Haymakers' Grounds	.
8	1871	NaN	WS3	OLY	NaN	4	32	NaN	15	15	...	371	4	45	13	217	NaN	0.85	Washington Olympics	Olympics Grounds	NaN
9	1872	NaN	BL1	BLC	NaN	2	58	NaN	35	19	...	566	3	63	0	432	NaN	0.82	Baltimore Canaries	Newington Park	NaN

10 rows × 43 columns

df.describe()

	Year	Final_Standing	Games_Played	Unnamed: 7	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	Doubles	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
count	2805.000000	2805.000000	2805.00000	2406.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	...	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2488.000000	2805.000000
mean	1955.036720	4.107308	150.34795	78.465919	74.749020	74.749020	681.945811	5142.492335	1346.273440	227.624955	...	9.664171	23.667736	4022.383244	1346.083779	101.136542	474.010695	731.229234	186.337255	140.186495	0.961519
std	41.519083	2.323414	23.22725	4.698684	17.640402	17.378079	135.738244	750.551691	219.891603	58.692602	...	5.097328	16.281300	630.996942	219.521064	58.245002	131.890032	296.409881	107.657444	29.322764	0.030224
min	1871.000000	1.000000	6.00000	44.000000	0.000000	4.000000	24.000000	211.000000	33.000000	3.000000	...	0.000000	0.000000	162.000000	49.000000	0.000000	0.000000	0.000000	47.000000	18.000000	0.760000
25%	1919.000000	2.000000	153.00000	77.000000	66.000000	65.000000	613.000000	5127.000000	1299.000000	193.000000	...	6.000000	9.000000	4077.000000	1288.000000	46.000000	427.000000	501.000000	116.000000	126.000000	0.960000
50%	1963.000000	4.000000	157.00000	81.000000	77.000000	76.000000	690.000000	5389.000000	1393.000000	231.000000	...	9.000000	24.000000	4236.000000	1392.000000	109.000000	494.000000	735.000000	145.000000	145.000000	0.970000
75%	1992.000000	6.000000	162.00000	81.000000	87.000000	87.000000	763.000000	5517.000000	1467.000000	270.000000	...	13.000000	38.000000	4341.000000	1470.000000	148.000000	555.000000	965.000000	217.000000	159.250000	0.980000
max	2015.000000	13.000000	165.00000	84.000000	116.000000	134.000000	1220.000000	5781.000000	1783.000000	376.000000	...	32.000000	68.000000	4518.000000	1993.000000	241.000000	827.000000	1450.000000	639.000000	217.000000	0.991000

8 rows × 32 columns

print(df.info())

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2805 entries, 0 to 2804
Data columns (total 43 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   Year                 2805 non-null   int64  
 1   League               2755 non-null   object 
 2   Team                 2805 non-null   object 
 3   Franchise            2805 non-null   object 
 4   Division             1288 non-null   object 
 5   Final_Standing       2805 non-null   int64  
 6   Games_Played         2805 non-null   int64  
 7   Unnamed: 7           2406 non-null   float64
 8   Games_Won            2805 non-null   int64  
 9   Games_Lost           2805 non-null   int64  
 10  Unnamed: 10          1260 non-null   object 
 11  Unnamed: 11          624 non-null    object 
 12  League_Win           2777 non-null   object 
 13  World_Series         2448 non-null   object 
 14  Runs_Scored          2805 non-null   int64  
 15  At_Bats              2805 non-null   int64  
 16  Hits                 2805 non-null   int64  
 17  Doubles              2805 non-null   int64  
 18  Triples              2805 non-null   int64  
 19  Home_Runs            2805 non-null   int64  
 20  Walks                2805 non-null   int64  
 21  Strike_Outs          2685 non-null   float64
 22  Stolen_Bases         2661 non-null   float64
 23  Caught_Stealing      1946 non-null   float64
 24  Hit_By_Pitch         480 non-null    float64
 25  Sacrifice_Fly        480 non-null    float64
 26  Runs_Against         2805 non-null   int64  
 27  Earned_Runs          2805 non-null   int64  
 28  Earned_Run_Average   2805 non-null   float64
 29  Complete_Games       2805 non-null   int64  
 30  Shutout              2805 non-null   int64  
 31  Saves                2805 non-null   int64  
 32  Infield_Put_Outs     2805 non-null   int64  
 33  Hits_Allowed         2805 non-null   int64  
 34  Home_Run_Allowed     2805 non-null   int64  
 35  Walks_Allowed        2805 non-null   int64  
 36  Strikeouts_Allowed   2805 non-null   int64  
 37  Errors               2805 non-null   int64  
 38  Double_Plays         2488 non-null   float64
 39  Fielding_Percentage  2805 non-null   float64
 40  Team_Name            2805 non-null   object 
 41  Home_Ball_Park       2771 non-null   object 
 42  Attendance           2527 non-null   object 
dtypes: float64(9), int64(23), object(11)
memory usage: 942.4+ KB
None

---

Navigate to:

Section 2 – Data Exploration
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---

Section 2.2. Completeness of Data

df.columns

Index(['Year', 'League', 'Team', 'Franchise ', 'Division', 'Final_Standing',
       'Games_Played', 'Unnamed: 7', 'Games_Won', 'Games_Lost', 'Unnamed: 10',
       'Unnamed: 11', 'League_Win', 'World_Series', 'Runs_Scored', 'At_Bats',
       'Hits', 'Doubles', 'Triples', 'Home_Runs', 'Walks', 'Strike_Outs',
       'Stolen_Bases', 'Caught_Stealing', 'Hit_By_Pitch', 'Sacrifice_Fly',
       'Runs_Against', 'Earned_Runs', 'Earned_Run_Average', 'Complete_Games',
       'Shutout', 'Saves', 'Infield_Put_Outs', 'Hits_Allowed',
       'Home_Run_Allowed', 'Walks_Allowed', 'Strikeouts_Allowed', 'Errors',
       'Double_Plays', 'Fielding_Percentage', 'Team_Name', 'Home_Ball_Park',
       'Attendance'],
      dtype='object')

From the information above, there are 2805 rows in total, which means each column needs to have 2805 entries for every columns. Only columns below have 2085 entries, so we'll keep them in the dataset

Year, Team, Franchise, Final Standing, Games_Played, Games_Won, Games_Lost, Runs_Scored, At_Bats, Hits, Doubles, Triples, Home_Runs, Walks, Runs_Against, Earned_Runs, Earned_Run_Average, Complete_Games, Shutout, Saves, Infield_Put_Outs, Hits_Allowed, Home_Run_Allowed, Walks_Allowed, Strikeouts_Allowed, Errors, Fielding_Percentage, Team_Name

The rest of the columns have some missing datas, so we now decide how we are going to do with it

First, there are 3 unnamed columns (Unnamed: 7, Unnamed: 10, Unnamed: 11), since the data itself (binary variables and discrete variables) cannot help us indentify the columns' name, we then remove the all 3 unnamed columns

Next, we have some missing data for the variables that describe style of play. The columns that have missing data are: Strike_Outs, Stolen_Bases, Caught_Stealing, Hit_By_Pitch, Sacrifice_Fly (Offensive Style) and Double Plays (Defensive Style)

Hit_By_Pitch and Sacrifice_Fly, only have 480 out of 2805 rows. Since there are too many missing rows so we will remove these 2 variables/columns from the dataset

Caught_Stealing only has 1946 out of 2805 entries. We will remove this column from the dataset

Strike_Out has full data from 1913 to 2015, so we can use this for period 3, 4 and the prediction

Stolen_Base has full data from 1886, so we can use this for period 2, 3, 4 and the prediction

Double_Plays has full data from 1900, so we can use this for period 2, 3, 4 and the prediction

We then also have other columns that have missing data. But those columns are either nominal variables (qualitative data) or have no affects on the Games Won (Dependent Variable). We can either replace the missing data with 0 or drop the columns; in this project, we decided to drop the columns. Those columns to be removed are League, Division, League_Win, World_Series, Home_Ball_Park, Attendance

Now, we are dropping the columns that are not necessary and have missing data

data_baseball=df.drop(['Sacrifice_Fly','Hit_By_Pitch','Unnamed: 7','Unnamed: 10','Unnamed: 11','League','Division', 'League_Win', 'World_Series', 'Home_Ball_Park', 'Attendance', 'Caught_Stealing'], axis='columns', inplace=False)

data_baseball.head()

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
0	1871	BS1	BNA	3	31	20	10	401	1372	426	...	3	828	367	2	42	23	225	NaN	0.83	Boston Red Stockings
1	1871	CH1	CNA	2	28	19	9	302	1196	323	...	1	753	308	6	28	22	218	NaN	0.82	Chicago White Stockings
2	1871	CL1	CFC	8	29	10	19	249	1186	328	...	0	762	346	13	53	34	223	NaN	0.81	Cleveland Forest Citys
3	1871	FW1	KEK	7	19	7	12	137	746	178	...	0	507	261	5	21	17	163	NaN	0.80	Fort Wayne Kekiongas
4	1871	NY2	NNA	5	33	16	17	302	1404	403	...	0	879	373	7	42	22	227	NaN	0.83	New York Mutuals

5 rows × 31 columns

data_baseball.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2805 entries, 0 to 2804
Data columns (total 31 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   Year                 2805 non-null   int64  
 1   Team                 2805 non-null   object 
 2   Franchise            2805 non-null   object 
 3   Final_Standing       2805 non-null   int64  
 4   Games_Played         2805 non-null   int64  
 5   Games_Won            2805 non-null   int64  
 6   Games_Lost           2805 non-null   int64  
 7   Runs_Scored          2805 non-null   int64  
 8   At_Bats              2805 non-null   int64  
 9   Hits                 2805 non-null   int64  
 10  Doubles              2805 non-null   int64  
 11  Triples              2805 non-null   int64  
 12  Home_Runs            2805 non-null   int64  
 13  Walks                2805 non-null   int64  
 14  Strike_Outs          2685 non-null   float64
 15  Stolen_Bases         2661 non-null   float64
 16  Runs_Against         2805 non-null   int64  
 17  Earned_Runs          2805 non-null   int64  
 18  Earned_Run_Average   2805 non-null   float64
 19  Complete_Games       2805 non-null   int64  
 20  Shutout              2805 non-null   int64  
 21  Saves                2805 non-null   int64  
 22  Infield_Put_Outs     2805 non-null   int64  
 23  Hits_Allowed         2805 non-null   int64  
 24  Home_Run_Allowed     2805 non-null   int64  
 25  Walks_Allowed        2805 non-null   int64  
 26  Strikeouts_Allowed   2805 non-null   int64  
 27  Errors               2805 non-null   int64  
 28  Double_Plays         2488 non-null   float64
 29  Fielding_Percentage  2805 non-null   float64
 30  Team_Name            2805 non-null   object 
dtypes: float64(5), int64(23), object(3)
memory usage: 679.5+ KB

After removing 12 columns, our dataset's columns decreased from 43 to 31

We now have the complete data, we can explore and determine data types provided in the complete dataset

Column Name	Data Type	Category
Year	Nominal	Descriptive Fields
Team	Nominal	Descriptive Fields
Franchise	Nominal	Descriptive Fields
Final_Standing	Discrete	Team Performance
Games_Played	Discrete	Team Performance
Games_Won	Discrete	Team Performance
Games_Lost	Discrete	Team Performance
Runs_Scored	Discrete	Team Performance
At_Bats	Discrete	Offensive Measurements
Hits	Discrete	Offensive Measurements
Doubles	Discrete	Offensive Measurements
Triples	Discrete	Offensive Measurements
Home_Runs	Discrete	Offensive Measurements
Walks	Discrete	Offensive Measurements
Strike_Outs	Discrete	Offensive Measurements
Stolen_Bases	Discrete	Offensive Measurements
Caught_Stealing	Discrete	removed
Hit_By_Pitch	Discrete	removed
Sacrifice_Fly	Discrete	removed
Runs_Against	Discrete	Defensive Measurements
Earned_Runs	Discrete	Defensive Measurements
Earned_Run_Average	Discrete	Defensive Measurements
Complete_Games	Discrete	Defensive Measurements
Shutout	Discrete	Defensive Measurements
Saves	Discrete	Defensive Measurements
Infield_Put_Outs	Discrete	Defensive Measurements
Hits_Allowed	Discrete	Defensive Measurements
Walks_Allowed	Discrete	Defensive Measurements
Strikeouts_Allowed	Discrete	Defensive Measurements
Errors	Discrete	Defensive Measurements
Double_Plays	Discrete	Defensive Measurements
Fielding_Percentage	Continious	Defensive Measurements
Team_Name	Nominal	Miscellaneous

As mentioned in the Objective, we are going to determine the style of play of each team during the years and how the style of play affects their chance to win.

The dependent variable is Games_Won

The potential independent variables that will be selected to build the model are all the columns that have either Offensive Measurements/Defensive Measurements in the Category in the table above

---

Navigate to:

Section 2 – Data Exploration
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---

Section 2.3. Does the Data Meet the Assumptions for Regression?

Checking Normality of the Independent Variables

data_baseball.describe()

	Year	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	Doubles	Triples	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
count	2805.000000	2805.000000	2805.00000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.00000	...	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2805.000000	2488.000000	2805.000000
mean	1955.036720	4.107308	150.34795	74.749020	74.749020	681.945811	5142.492335	1346.273440	227.624955	47.10410	...	9.664171	23.667736	4022.383244	1346.083779	101.136542	474.010695	731.229234	186.337255	140.186495	0.961519
std	41.519083	2.323414	23.22725	17.640402	17.378079	135.738244	750.551691	219.891603	58.692602	22.26862	...	5.097328	16.281300	630.996942	219.521064	58.245002	131.890032	296.409881	107.657444	29.322764	0.030224
min	1871.000000	1.000000	6.00000	0.000000	4.000000	24.000000	211.000000	33.000000	3.000000	0.00000	...	0.000000	0.000000	162.000000	49.000000	0.000000	0.000000	0.000000	47.000000	18.000000	0.760000
25%	1919.000000	2.000000	153.00000	66.000000	65.000000	613.000000	5127.000000	1299.000000	193.000000	31.00000	...	6.000000	9.000000	4077.000000	1288.000000	46.000000	427.000000	501.000000	116.000000	126.000000	0.960000
50%	1963.000000	4.000000	157.00000	77.000000	76.000000	690.000000	5389.000000	1393.000000	231.000000	41.00000	...	9.000000	24.000000	4236.000000	1392.000000	109.000000	494.000000	735.000000	145.000000	145.000000	0.970000
75%	1992.000000	6.000000	162.00000	87.000000	87.000000	763.000000	5517.000000	1467.000000	270.000000	60.00000	...	13.000000	38.000000	4341.000000	1470.000000	148.000000	555.000000	965.000000	217.000000	159.250000	0.980000
max	2015.000000	13.000000	165.00000	116.000000	134.000000	1220.000000	5781.000000	1783.000000	376.000000	150.00000	...	32.000000	68.000000	4518.000000	1993.000000	241.000000	827.000000	1450.000000	639.000000	217.000000	0.991000

8 rows × 28 columns

Offensive Measurements

data_baseball.columns

Index(['Year', 'Team', 'Franchise ', 'Final_Standing', 'Games_Played',
       'Games_Won', 'Games_Lost', 'Runs_Scored', 'At_Bats', 'Hits', 'Doubles',
       'Triples', 'Home_Runs', 'Walks', 'Strike_Outs', 'Stolen_Bases',
       'Runs_Against', 'Earned_Runs', 'Earned_Run_Average', 'Complete_Games',
       'Shutout', 'Saves', 'Infield_Put_Outs', 'Hits_Allowed',
       'Home_Run_Allowed', 'Walks_Allowed', 'Strikeouts_Allowed', 'Errors',
       'Double_Plays', 'Fielding_Percentage', 'Team_Name'],
      dtype='object')

offensive = ['Runs_Scored', 'At_Bats', 'Hits', 'Doubles',
       'Triples', 'Home_Runs', 'Walks', 'Strike_Outs', 'Stolen_Bases']
for i in offensive:
    qqplot(data_baseball[i],line='s')
    plt.title(label=i)

All of them are not normal distribution except Double & Runs_Scored. Data from these 2 variable is is not precisely normal, but not too far off.

Defensive Measurements

defensive = ['Runs_Against',
       'Earned_Runs', 'Earned_Run_Average', 'Complete_Games', 'Shutout',
       'Saves', 'Infield_Put_Outs', 'Hits_Allowed', 'Home_Run_Allowed',
       'Walks_Allowed', 'Strikeouts_Allowed', 'Errors', 'Double_Plays',
       'Fielding_Percentage']
for i in defensive:
    qqplot(data_baseball[i],line='s')
    plt.title(label=i)

All of them are not normal distribution except Earned_Run_Average. Data from Earned_Run_Average variable is is not precisely normal, but not too far off.

Since most of data from the variables are not normally distributed, we will use Spearman method to calculate the correlation

Checking if Independent variables are independent of each other

data_baseball.corr(method='spearman',numeric_only=True)

	Year	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	Doubles	Triples	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
Year	1.000000	-0.274699	0.781980	0.315051	0.340399	0.240707	0.766968	0.432009	0.678671	-0.631983	...	0.097021	0.892868	0.743554	0.422593	0.865201	0.458994	0.883236	-0.888545	0.361047	0.916595
Final_Standing	-0.274699	1.000000	-0.213166	-0.801612	0.640538	-0.459954	-0.252544	-0.344243	-0.334162	0.088824	...	-0.372299	-0.390545	-0.290483	0.186951	-0.145467	0.107300	-0.326219	0.341624	-0.014340	-0.338664
Games_Played	0.781980	-0.213166	1.000000	0.426088	0.395069	0.240833	0.866048	0.472664	0.548309	-0.434139	...	0.258410	0.786178	0.931249	0.445805	0.720693	0.464576	0.816380	-0.632648	0.354613	0.714013
Games_Won	0.315051	-0.801612	0.426088	1.000000	-0.476318	0.575551	0.450319	0.537469	0.434675	0.013223	...	0.536561	0.491225	0.510420	-0.010287	0.234248	0.051055	0.424356	-0.356374	0.142152	0.408746
Games_Lost	0.340399	0.640538	0.395069	-0.476318	1.000000	-0.226362	0.327896	0.051015	0.167462	-0.159084	...	-0.179071	0.181630	0.286110	0.588136	0.412657	0.513484	0.258669	-0.141217	0.223401	0.232301
Runs_Scored	0.240707	-0.459954	0.240833	0.575551	-0.226362	1.000000	0.468626	0.757546	0.616222	0.132385	...	-0.069142	0.298107	0.219980	0.411270	0.375124	0.272330	0.226619	-0.197410	0.352792	0.261518
At_Bats	0.766968	-0.252544	0.866048	0.450319	0.327896	0.468626	1.000000	0.742428	0.732729	-0.366264	...	0.121713	0.755724	0.859493	0.603994	0.759212	0.495107	0.740341	-0.631324	0.461246	0.717702
Hits	0.432009	-0.344243	0.472664	0.537469	0.051015	0.757546	0.742428	1.000000	0.785740	0.022698	...	0.029691	0.459474	0.456512	0.643577	0.486024	0.366194	0.342793	-0.363469	0.405722	0.446763
Doubles	0.678671	-0.334162	0.548309	0.434675	0.167462	0.616222	0.732729	0.785740	1.000000	-0.220792	...	0.004934	0.623705	0.513107	0.617070	0.650222	0.422942	0.560636	-0.581621	0.366630	0.661537
Triples	-0.631983	0.088824	-0.434139	0.013223	-0.159084	0.132385	-0.366264	0.022698	-0.220792	1.000000	...	0.051694	-0.551959	-0.414802	-0.068064	-0.551999	-0.198915	-0.565666	0.635171	-0.191162	-0.559284
Home_Runs	0.823918	-0.347434	0.693135	0.450463	0.179379	0.512871	0.757164	0.541482	0.660915	-0.532944	...	0.045617	0.803792	0.662230	0.439857	0.886188	0.499955	0.778469	-0.764482	0.433687	0.792145
Walks	0.461719	-0.305729	0.483255	0.490243	0.082485	0.539667	0.490052	0.447216	0.490117	-0.199808	...	0.118947	0.508623	0.487373	0.366321	0.525874	0.545336	0.447933	-0.434163	0.378155	0.478526
Strike_Outs	0.895568	-0.200366	0.813299	0.302005	0.402110	0.154026	0.719682	0.259131	0.530377	-0.566149	...	0.180225	0.825208	0.772673	0.312014	0.822780	0.431565	0.920380	-0.745329	0.229025	0.797131
Stolen_Bases	-0.192581	-0.082728	-0.063741	0.048425	-0.137192	0.080899	-0.176351	-0.131850	-0.175577	0.304038	...	0.029598	-0.143803	-0.051383	-0.205197	-0.289459	-0.221423	-0.080675	0.296674	-0.342434	-0.286610
Runs_Against	0.253098	0.355105	0.223545	-0.242123	0.600748	0.439777	0.376841	0.438892	0.442703	0.019831	...	-0.500155	0.139218	0.097777	0.794766	0.479119	0.551323	0.126411	-0.066519	0.379589	0.161943
Earned_Runs	0.595115	0.168519	0.498714	-0.046020	0.619575	0.431541	0.636378	0.578177	0.663727	-0.257239	...	-0.342406	0.478491	0.385637	0.868230	0.762225	0.673869	0.429312	-0.448664	0.484250	0.524027
Earned_Run_Average	0.387392	0.305546	0.189396	-0.274268	0.500262	0.350832	0.356915	0.401457	0.485021	-0.207851	...	-0.566322	0.243548	0.066119	0.732008	0.579502	0.521991	0.176583	-0.300424	0.404286	0.312411
Complete_Games	-0.907837	0.185047	-0.661237	-0.136375	-0.286972	-0.127545	-0.658504	-0.312849	-0.578901	0.719088	...	0.085239	-0.842178	-0.620513	-0.353932	-0.802188	-0.406879	-0.784269	0.838758	-0.321861	-0.810418
Shutout	0.097021	-0.372299	0.258410	0.536561	-0.179071	-0.069142	0.121713	0.029691	0.004934	0.051694	...	1.000000	0.180824	0.336574	-0.271823	-0.070023	-0.093790	0.246854	-0.136851	-0.090311	0.182850
Saves	0.892868	-0.390545	0.786178	0.491225	0.181630	0.298107	0.755724	0.459474	0.623705	-0.551959	...	0.180824	1.000000	0.787709	0.337349	0.785848	0.424078	0.844665	-0.814831	0.349019	0.834160
Infield_Put_Outs	0.743554	-0.290483	0.931249	0.510420	0.286110	0.219980	0.859493	0.456512	0.513107	-0.414802	...	0.336574	0.787709	1.000000	0.358175	0.650998	0.404665	0.802176	-0.618994	0.325047	0.697420
Hits_Allowed	0.422593	0.186951	0.445805	-0.010287	0.588136	0.411270	0.603994	0.643577	0.617070	-0.068064	...	-0.271823	0.337349	0.358175	1.000000	0.550584	0.469565	0.238806	-0.254858	0.454944	0.364834
Home_Run_Allowed	0.865201	-0.145467	0.720693	0.234248	0.412657	0.375124	0.759212	0.486024	0.650222	-0.551999	...	-0.070023	0.785848	0.650998	0.550584	1.000000	0.557030	0.781631	-0.772648	0.449520	0.805396
Walks_Allowed	0.458994	0.107300	0.464576	0.051055	0.513484	0.272330	0.495107	0.366194	0.422942	-0.198915	...	-0.093790	0.424078	0.404665	0.469565	0.557030	1.000000	0.420674	-0.355897	0.489310	0.410029
Strikeouts_Allowed	0.883236	-0.326219	0.816380	0.424356	0.258669	0.226619	0.740341	0.342793	0.560636	-0.565666	...	0.246854	0.844665	0.802176	0.238806	0.781631	0.420674	1.000000	-0.769876	0.215895	0.811301
Errors	-0.888545	0.341624	-0.632648	-0.356374	-0.141217	-0.197410	-0.631324	-0.363469	-0.581621	0.635171	...	-0.136851	-0.814831	-0.618994	-0.254858	-0.772648	-0.355897	-0.769876	1.000000	-0.346504	-0.933260
Double_Plays	0.361047	-0.014340	0.354613	0.142152	0.223401	0.352792	0.461246	0.405722	0.366630	-0.191162	...	-0.090311	0.349019	0.325047	0.454944	0.449520	0.489310	0.215895	-0.346504	1.000000	0.393810
Fielding_Percentage	0.916595	-0.338664	0.714013	0.408746	0.232301	0.261518	0.717702	0.446763	0.661537	-0.559284	...	0.182850	0.834160	0.697420	0.364834	0.805396	0.410029	0.811301	-0.933260	0.393810	1.000000

28 rows × 28 columns

print(data_baseball.corr(method='spearman',numeric_only=True)['Games_Won'].sort_values(ascending=False))

Games_Won              1.000000
Runs_Scored            0.575551
Hits                   0.537469
Shutout                0.536561
Infield_Put_Outs       0.510420
Saves                  0.491225
Walks                  0.490243
Home_Runs              0.450463
At_Bats                0.450319
Doubles                0.434675
Games_Played           0.426088
Strikeouts_Allowed     0.424356
Fielding_Percentage    0.408746
Year                   0.315051
Strike_Outs            0.302005
Home_Run_Allowed       0.234248
Double_Plays           0.142152
Walks_Allowed          0.051055
Stolen_Bases           0.048425
Triples                0.013223
Hits_Allowed          -0.010287
Earned_Runs           -0.046020
Complete_Games        -0.136375
Runs_Against          -0.242123
Earned_Run_Average    -0.274268
Errors                -0.356374
Games_Lost            -0.476318
Final_Standing        -0.801612
Name: Games_Won, dtype: float64

Some independent variables are dependent of each other (correlation is over 0.7)

• Hits has strong correlations with Doubles (0.79), Runs_Scored (0.76), At_Bats (0.74),
• At_Bats has strong correlations with Infield_Put_Outs (0.86), Saves (0.76), Home_Run_Allowed (0.76), Home_Runs 0.76), Strikeouts_Allowed (0.74), Hits (0.74), Doubles (0.73), Fielding_Percentage (0.72), and Strike_Outs (0.72)
• Home_Runs has strong correlations with Home_Run_Allowed (0.89),Saves (0.8),Strikeouts_Allowed (0.78), , Fielding_Percentage (0.79), Strike_Outs (0.79), At Bats (0.76), Complete_Games (-0.74), Errors (-0.76)
• Strike_Outs has strong correlations with Strikeouts_Allowed (0.92), Saves (0.83), Home_Run_Allowed (0.82), Fielding_Percentage (0.8), Home_Runs (0.79), Infield_Put_Outs (0.77), At_Bats (0.72)
• Runs_Against has strong correlations with Earned_Run_Average (0.87), Earned_Runs (0.86), Hits_Allowed (0.79)
• Earned_Runs has strong correlations with Earned_Run_Average (0.89), Hits_Allowed (0.87), Runs_Against (0.86), Home_Run_Allowed (0.76)
• Complete_Games has strong correlations with Errors (0.84), Triples (0.72), Home_Runs (-0.74), Strikeouts_Allowed (-0.78), Home_Run_Allowed (-0.8), Fielding_Percentage (-0.81), Strike_Outs (-0.82), Saves (-0.84)
• Saves has strong correlations with Home_Runs (0.8), Infield_Put_Outs (0.79), Home_Run_Allowed (0.79), Strike_Outs (0.77), At_Bats (0.76)
• Hits_Allowed has strong correlations with Earned_Runs (0.87), Runs_Against (0.79), Earned_Run_Average (0.73)
• Home_Run_Allowed has strong correlations with Home_Runs (0.89), Strike_Outs (0.82), Fielding_Percentage (0.81), Strikeouts_Allowed (0.78), Saves (0.79), At Bats (0.76), Earned_Runs (0.76), Errors (-0.77), and Complete_Games (-0.8)
• Strikeouts_Allowed has strong correlations Strike_Outs (0.92), , Saves (0.84), Fielding_Percentage (0.81), Infield_Put_Outs (0.8), Home_Run_Allowed (0.78), Home_Runs (0.78), At_Bats (0.74), Complete_Games (-0.78), Errors (-0.77)
• Errors has strong correlations with Complete_Games (0.84), Strike_Outs (-0.75), Home_Runs (-0.76), Home_Run_Allowed (-0.77), Strikeouts_Allowed (-0.77), Saves (-0.81), Fielding_Percentage (-0.93)

Variables that are not dependent of other independent variables: Walks, Stolen_Bases, Shutout, Walks_Allowed, Double Plays

Assuming we use data of the entire data set to build the model, top 8 independent variables that the biggest correlations are Runs_Scored, Hits, Shutout, Infield_Put_Outs, Saves, Walks, Home_Runs, At_Bats. We can first keep Shutout, Walks because these 2 variables are not dependent of any other independent variables. Between Runs_Scored, Hits, Saves, Walks, Home_Runs, and At_Bats, since these are highly dependent of each other, we can only keep maximum 2 of them

Because this is a general data analysis for the entire data set, we will not eliminate these variables from the dataset for now, but we will keep it into conderation when choosing top 8 variables to build the regression models. If there are independent variables that have high correlation with others in top 8 list, we can only keep one of them in the model

Checking if Independent variables are linearly related to the dependent variable

Offensive Measurements

offensive = ['Runs_Scored', 'At_Bats', 'Hits', 'Doubles',
       'Triples', 'Home_Runs', 'Walks', 'Strike_Outs', 'Stolen_Bases']
for i in offensive:
    sns.scatterplot(data_baseball,x=i,y='Games_Won')
    plt.show()

Independent variables that don't have a linear relatinship to the dependent variable are Stolen Bases, Triples

Defensive Measurements

for i in defensive:
    sns.scatterplot(data_baseball,x=i,y='Games_Won')
    plt.show()

Independent variables that don't have a linear relatinship to the dependent variable Runs_Against, Home_Run_Allowed, Earned_Run, Earned Run Average, Double Play, Complete Games, Hits_Allowed

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Section 2.4. Data Exploration - Conclusion Summary

Column Name	Data Type	Category	Normality	# of missing values	Action
Year	Nominal	Descriptive Fields
Team	Nominal	Descriptive Fields
Franchise	Nominal	Descriptive Fields
Final_Standing	Discrete	Team Performance
Games_Played	Discrete	Team Performance
Games_Won	Discrete	Team Performance
Games_Lost	Discrete	Team Performance
Runs_Scored	Discrete	Team Performance	Yes
At_Bats	Discrete	Offensive Measurements
Hits	Discrete	Offensive Measurements
Doubles	Discrete	Offensive Measurements	Yes
Triples	Discrete	Offensive Measurements
Home_Runs	Discrete	Offensive Measurements
Walks	Discrete	Offensive Measurements
Strike_Outs	Discrete	Offensive Measurements		120	used for period 3, 4
Stolen_Bases	Discrete	Offensive Measurements		144	used for period 2, 3, 4
Caught_Stealing	Discrete	Offensive Measurements		859	to be removed
Hit_By_Pitch	Discrete	Offensive Measurements		2325	to be removed
Sacrifice_Fly	Discrete	Offensive Measurements		2325	to be removed
Runs_Against	Discrete	Defensive Measurements
Earned_Runs	Discrete	Defensive Measurements
Earned_Run_Average	Discrete	Defensive Measurements	Yes
Complete_Games	Discrete	Defensive Measurements
Shutout	Discrete	Defensive Measurements
Saves	Discrete	Defensive Measurements
Infield_Put_Outs	Discrete	Defensive Measurements
Hits_Allowed	Discrete	Defensive Measurements
Walks_Allowed	Discrete	Defensive Measurements
Strikeouts_Allowed	Discrete	Defensive Measurements
Errors	Discrete	Defensive Measurements
Double_Plays	Discrete	Defensive Measurements		317	used for period 2, 3, 4
Fielding_Percentage	Continious	Defensive Measurements
Team_Name	Nominal	Miscellaneous

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Section 3 – Correlation Analysis

data_baseball.corr(method='spearman',numeric_only=True)

	Year	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	Doubles	Triples	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
Year	1.000000	-0.274699	0.781980	0.315051	0.340399	0.240707	0.766968	0.432009	0.678671	-0.631983	...	0.097021	0.892868	0.743554	0.422593	0.865201	0.458994	0.883236	-0.888545	0.361047	0.916595
Final_Standing	-0.274699	1.000000	-0.213166	-0.801612	0.640538	-0.459954	-0.252544	-0.344243	-0.334162	0.088824	...	-0.372299	-0.390545	-0.290483	0.186951	-0.145467	0.107300	-0.326219	0.341624	-0.014340	-0.338664
Games_Played	0.781980	-0.213166	1.000000	0.426088	0.395069	0.240833	0.866048	0.472664	0.548309	-0.434139	...	0.258410	0.786178	0.931249	0.445805	0.720693	0.464576	0.816380	-0.632648	0.354613	0.714013
Games_Won	0.315051	-0.801612	0.426088	1.000000	-0.476318	0.575551	0.450319	0.537469	0.434675	0.013223	...	0.536561	0.491225	0.510420	-0.010287	0.234248	0.051055	0.424356	-0.356374	0.142152	0.408746
Games_Lost	0.340399	0.640538	0.395069	-0.476318	1.000000	-0.226362	0.327896	0.051015	0.167462	-0.159084	...	-0.179071	0.181630	0.286110	0.588136	0.412657	0.513484	0.258669	-0.141217	0.223401	0.232301
Runs_Scored	0.240707	-0.459954	0.240833	0.575551	-0.226362	1.000000	0.468626	0.757546	0.616222	0.132385	...	-0.069142	0.298107	0.219980	0.411270	0.375124	0.272330	0.226619	-0.197410	0.352792	0.261518
At_Bats	0.766968	-0.252544	0.866048	0.450319	0.327896	0.468626	1.000000	0.742428	0.732729	-0.366264	...	0.121713	0.755724	0.859493	0.603994	0.759212	0.495107	0.740341	-0.631324	0.461246	0.717702
Hits	0.432009	-0.344243	0.472664	0.537469	0.051015	0.757546	0.742428	1.000000	0.785740	0.022698	...	0.029691	0.459474	0.456512	0.643577	0.486024	0.366194	0.342793	-0.363469	0.405722	0.446763
Doubles	0.678671	-0.334162	0.548309	0.434675	0.167462	0.616222	0.732729	0.785740	1.000000	-0.220792	...	0.004934	0.623705	0.513107	0.617070	0.650222	0.422942	0.560636	-0.581621	0.366630	0.661537
Triples	-0.631983	0.088824	-0.434139	0.013223	-0.159084	0.132385	-0.366264	0.022698	-0.220792	1.000000	...	0.051694	-0.551959	-0.414802	-0.068064	-0.551999	-0.198915	-0.565666	0.635171	-0.191162	-0.559284
Home_Runs	0.823918	-0.347434	0.693135	0.450463	0.179379	0.512871	0.757164	0.541482	0.660915	-0.532944	...	0.045617	0.803792	0.662230	0.439857	0.886188	0.499955	0.778469	-0.764482	0.433687	0.792145
Walks	0.461719	-0.305729	0.483255	0.490243	0.082485	0.539667	0.490052	0.447216	0.490117	-0.199808	...	0.118947	0.508623	0.487373	0.366321	0.525874	0.545336	0.447933	-0.434163	0.378155	0.478526
Strike_Outs	0.895568	-0.200366	0.813299	0.302005	0.402110	0.154026	0.719682	0.259131	0.530377	-0.566149	...	0.180225	0.825208	0.772673	0.312014	0.822780	0.431565	0.920380	-0.745329	0.229025	0.797131
Stolen_Bases	-0.192581	-0.082728	-0.063741	0.048425	-0.137192	0.080899	-0.176351	-0.131850	-0.175577	0.304038	...	0.029598	-0.143803	-0.051383	-0.205197	-0.289459	-0.221423	-0.080675	0.296674	-0.342434	-0.286610
Runs_Against	0.253098	0.355105	0.223545	-0.242123	0.600748	0.439777	0.376841	0.438892	0.442703	0.019831	...	-0.500155	0.139218	0.097777	0.794766	0.479119	0.551323	0.126411	-0.066519	0.379589	0.161943
Earned_Runs	0.595115	0.168519	0.498714	-0.046020	0.619575	0.431541	0.636378	0.578177	0.663727	-0.257239	...	-0.342406	0.478491	0.385637	0.868230	0.762225	0.673869	0.429312	-0.448664	0.484250	0.524027
Earned_Run_Average	0.387392	0.305546	0.189396	-0.274268	0.500262	0.350832	0.356915	0.401457	0.485021	-0.207851	...	-0.566322	0.243548	0.066119	0.732008	0.579502	0.521991	0.176583	-0.300424	0.404286	0.312411
Complete_Games	-0.907837	0.185047	-0.661237	-0.136375	-0.286972	-0.127545	-0.658504	-0.312849	-0.578901	0.719088	...	0.085239	-0.842178	-0.620513	-0.353932	-0.802188	-0.406879	-0.784269	0.838758	-0.321861	-0.810418
Shutout	0.097021	-0.372299	0.258410	0.536561	-0.179071	-0.069142	0.121713	0.029691	0.004934	0.051694	...	1.000000	0.180824	0.336574	-0.271823	-0.070023	-0.093790	0.246854	-0.136851	-0.090311	0.182850
Saves	0.892868	-0.390545	0.786178	0.491225	0.181630	0.298107	0.755724	0.459474	0.623705	-0.551959	...	0.180824	1.000000	0.787709	0.337349	0.785848	0.424078	0.844665	-0.814831	0.349019	0.834160
Infield_Put_Outs	0.743554	-0.290483	0.931249	0.510420	0.286110	0.219980	0.859493	0.456512	0.513107	-0.414802	...	0.336574	0.787709	1.000000	0.358175	0.650998	0.404665	0.802176	-0.618994	0.325047	0.697420
Hits_Allowed	0.422593	0.186951	0.445805	-0.010287	0.588136	0.411270	0.603994	0.643577	0.617070	-0.068064	...	-0.271823	0.337349	0.358175	1.000000	0.550584	0.469565	0.238806	-0.254858	0.454944	0.364834
Home_Run_Allowed	0.865201	-0.145467	0.720693	0.234248	0.412657	0.375124	0.759212	0.486024	0.650222	-0.551999	...	-0.070023	0.785848	0.650998	0.550584	1.000000	0.557030	0.781631	-0.772648	0.449520	0.805396
Walks_Allowed	0.458994	0.107300	0.464576	0.051055	0.513484	0.272330	0.495107	0.366194	0.422942	-0.198915	...	-0.093790	0.424078	0.404665	0.469565	0.557030	1.000000	0.420674	-0.355897	0.489310	0.410029
Strikeouts_Allowed	0.883236	-0.326219	0.816380	0.424356	0.258669	0.226619	0.740341	0.342793	0.560636	-0.565666	...	0.246854	0.844665	0.802176	0.238806	0.781631	0.420674	1.000000	-0.769876	0.215895	0.811301
Errors	-0.888545	0.341624	-0.632648	-0.356374	-0.141217	-0.197410	-0.631324	-0.363469	-0.581621	0.635171	...	-0.136851	-0.814831	-0.618994	-0.254858	-0.772648	-0.355897	-0.769876	1.000000	-0.346504	-0.933260
Double_Plays	0.361047	-0.014340	0.354613	0.142152	0.223401	0.352792	0.461246	0.405722	0.366630	-0.191162	...	-0.090311	0.349019	0.325047	0.454944	0.449520	0.489310	0.215895	-0.346504	1.000000	0.393810
Fielding_Percentage	0.916595	-0.338664	0.714013	0.408746	0.232301	0.261518	0.717702	0.446763	0.661537	-0.559284	...	0.182850	0.834160	0.697420	0.364834	0.805396	0.410029	0.811301	-0.933260	0.393810	1.000000

28 rows × 28 columns

Section 3.1. Correlation Analysis of Period 1 - before 1920

As mentioned in Section 2: Data Exploration, there is no data for Strike_Out, Stolen_Base, Double_Plays for this Period so we will remove it from Period 1 Correlation Calculation to determine style of Play

data_baseball_1=data_baseball[data_baseball['Year']<1920]
data_baseball_1=data_baseball_1.drop(['Franchise ','Final_Standing','Games_Played','Games_Lost','Strike_Outs','Stolen_Bases','Double_Plays'], axis='columns', inplace=False)
data_baseball_1.head(5)

	Year	Team	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Fielding_Percentage	Team_Name
0	1871	BS1	20	401	1372	426	70	37	3	60	...	1	3	828	367	2	42	23	225	0.83	Boston Red Stockings
1	1871	CH1	19	302	1196	323	52	21	10	60	...	0	1	753	308	6	28	22	218	0.82	Chicago White Stockings
2	1871	CL1	10	249	1186	328	35	40	7	26	...	0	0	762	346	13	53	34	223	0.81	Cleveland Forest Citys
3	1871	FW1	7	137	746	178	19	8	2	33	...	1	0	507	261	5	21	17	163	0.80	Fort Wayne Kekiongas
4	1871	NY2	16	302	1404	403	43	21	1	33	...	1	0	879	373	7	42	22	227	0.83	New York Mutuals

5 rows × 24 columns

data_baseball_1.info()

<class 'pandas.core.frame.DataFrame'>
Index: 703 entries, 0 to 702
Data columns (total 24 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   Year                 703 non-null    int64  
 1   Team                 703 non-null    object 
 2   Games_Won            703 non-null    int64  
 3   Runs_Scored          703 non-null    int64  
 4   At_Bats              703 non-null    int64  
 5   Hits                 703 non-null    int64  
 6   Doubles              703 non-null    int64  
 7   Triples              703 non-null    int64  
 8   Home_Runs            703 non-null    int64  
 9   Walks                703 non-null    int64  
 10  Runs_Against         703 non-null    int64  
 11  Earned_Runs          703 non-null    int64  
 12  Earned_Run_Average   703 non-null    float64
 13  Complete_Games       703 non-null    int64  
 14  Shutout              703 non-null    int64  
 15  Saves                703 non-null    int64  
 16  Infield_Put_Outs     703 non-null    int64  
 17  Hits_Allowed         703 non-null    int64  
 18  Home_Run_Allowed     703 non-null    int64  
 19  Walks_Allowed        703 non-null    int64  
 20  Strikeouts_Allowed   703 non-null    int64  
 21  Errors               703 non-null    int64  
 22  Fielding_Percentage  703 non-null    float64
 23  Team_Name            703 non-null    object 
dtypes: float64(2), int64(20), object(2)
memory usage: 137.3+ KB

data_baseball_1.corr(method='spearman',numeric_only=True)

	Year	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	Runs_Against	...	Complete_Games	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Fielding_Percentage
Year	1.000000	0.553107	0.107374	0.725220	0.551325	0.503047	0.376502	0.290436	0.589186	0.151924	...	0.071586	0.648692	0.760274	0.849696	0.557399	0.286971	0.589335	0.624425	-0.612668	0.939038
Games_Won	0.553107	1.000000	0.609485	0.635757	0.700850	0.664230	0.567015	0.486563	0.621796	0.029506	...	0.374354	0.691273	0.592741	0.671723	0.269425	0.233305	0.358365	0.616015	-0.304828	0.661324
Runs_Scored	0.107374	0.609485	1.000000	0.399262	0.758286	0.672725	0.710060	0.723392	0.632252	0.587389	...	0.550255	0.058647	0.212410	0.233997	0.490005	0.558994	0.466616	0.216825	0.300881	0.136364
At_Bats	0.725220	0.635757	0.399262	1.000000	0.762945	0.585992	0.534613	0.411831	0.654047	0.379451	...	0.413958	0.552729	0.585054	0.922037	0.686776	0.396297	0.665916	0.666052	-0.264247	0.716559
Hits	0.551325	0.700850	0.758286	0.762945	1.000000	0.790539	0.731218	0.645367	0.693361	0.531624	...	0.437852	0.317448	0.505305	0.625373	0.726588	0.529074	0.620909	0.400532	-0.124616	0.558742
Doubles	0.503047	0.664230	0.672725	0.585992	0.790539	1.000000	0.579910	0.629602	0.615677	0.410463	...	0.327829	0.339055	0.485716	0.529576	0.566666	0.472718	0.509094	0.437182	-0.123000	0.511970
Triples	0.376502	0.567015	0.710060	0.534613	0.731218	0.579910	1.000000	0.614107	0.564460	0.495821	...	0.425980	0.207482	0.355576	0.435812	0.538966	0.462890	0.519937	0.333154	0.042551	0.373548
Home_Runs	0.290436	0.486563	0.723392	0.411831	0.645367	0.629602	0.614107	1.000000	0.543065	0.545591	...	0.409652	0.128568	0.279401	0.309350	0.489662	0.736548	0.500267	0.308907	0.141524	0.272651
Walks	0.589186	0.621796	0.632252	0.654047	0.693361	0.615677	0.564460	0.543065	1.000000	0.512543	...	0.330158	0.332029	0.571187	0.640106	0.628274	0.530233	0.759536	0.475956	-0.122523	0.561203
Runs_Against	0.151924	0.029506	0.587389	0.379451	0.531624	0.410463	0.495821	0.545591	0.512543	1.000000	...	0.537418	-0.247444	0.038756	0.200833	0.779524	0.726317	0.658181	0.092933	0.464460	0.036327
Earned_Runs	0.393301	0.148052	0.555897	0.522213	0.645120	0.512410	0.540154	0.565534	0.613799	0.925430	...	0.457378	-0.092804	0.236398	0.380888	0.898591	0.740567	0.756082	0.170635	0.182002	0.293383
Earned_Run_Average	-0.174014	-0.378637	0.251076	-0.087315	0.160704	0.071842	0.159267	0.248767	0.137329	0.726633	...	0.140010	-0.633984	-0.241579	-0.259810	0.451578	0.472831	0.300310	-0.348346	0.340818	-0.292012
Complete_Games	0.071586	0.374354	0.550255	0.413958	0.437852	0.327829	0.425980	0.409652	0.330158	0.537418	...	1.000000	0.171669	-0.114333	0.291003	0.427003	0.419993	0.312632	0.291597	0.337331	0.136295
Shutout	0.648692	0.691273	0.058647	0.552729	0.317448	0.339055	0.207482	0.128568	0.332029	-0.247444	...	0.171669	1.000000	0.564568	0.707844	0.092116	-0.019406	0.214127	0.675962	-0.489450	0.736280
Saves	0.760274	0.592741	0.212410	0.585054	0.505305	0.485716	0.355576	0.279401	0.571187	0.038756	...	-0.114333	0.564568	1.000000	0.702414	0.372415	0.204592	0.496895	0.540862	-0.500914	0.745408
Infield_Put_Outs	0.849696	0.671723	0.233997	0.922037	0.625373	0.529576	0.435812	0.309350	0.640106	0.200833	...	0.291003	0.707844	0.702414	1.000000	0.573955	0.293877	0.614096	0.766730	-0.436475	0.849280
Hits_Allowed	0.557399	0.269425	0.490005	0.686776	0.726588	0.566666	0.538966	0.489662	0.628274	0.779524	...	0.427003	0.092116	0.372415	0.573955	1.000000	0.629721	0.701395	0.267022	-0.006595	0.467880
Home_Run_Allowed	0.286971	0.233305	0.558994	0.396297	0.529074	0.472718	0.462890	0.736548	0.530233	0.726317	...	0.419993	-0.019406	0.204592	0.293877	0.629721	1.000000	0.551652	0.234406	0.207336	0.228728
Walks_Allowed	0.589335	0.358365	0.466616	0.665916	0.620909	0.509094	0.519937	0.500267	0.759536	0.658181	...	0.312632	0.214127	0.496895	0.614096	0.701395	0.551652	1.000000	0.446855	-0.051443	0.506870
Strikeouts_Allowed	0.624425	0.616015	0.216825	0.666052	0.400532	0.437182	0.333154	0.308907	0.475956	0.092933	...	0.291597	0.675962	0.540862	0.766730	0.267022	0.234406	0.446855	1.000000	-0.241414	0.629396
Errors	-0.612668	-0.304828	0.300881	-0.264247	-0.124616	-0.123000	0.042551	0.141524	-0.122523	0.464460	...	0.337331	-0.489450	-0.500914	-0.436475	-0.006595	0.207336	-0.051443	-0.241414	1.000000	-0.697764
Fielding_Percentage	0.939038	0.661324	0.136364	0.716559	0.558742	0.511970	0.373548	0.272651	0.561203	0.036327	...	0.136295	0.736280	0.745408	0.849280	0.467880	0.228728	0.506870	0.629396	-0.697764	1.000000

22 rows × 22 columns

df1_corr = data_baseball_1.corr(method='spearman',numeric_only=True)
print(df1_corr['Games_Won'].sort_values(ascending=False))

Games_Won              1.000000
Hits                   0.700850
Shutout                0.691273
Infield_Put_Outs       0.671723
Doubles                0.664230
Fielding_Percentage    0.661324
At_Bats                0.635757
Walks                  0.621796
Strikeouts_Allowed     0.616015
Runs_Scored            0.609485
Saves                  0.592741
Triples                0.567015
Year                   0.553107
Home_Runs              0.486563
Complete_Games         0.374354
Walks_Allowed          0.358365
Hits_Allowed           0.269425
Home_Run_Allowed       0.233305
Earned_Runs            0.148052
Runs_Against           0.029506
Errors                -0.304828
Earned_Run_Average    -0.378637
Name: Games_Won, dtype: float64

Top 8 variables that have the highest correlation with Games Won are Hits (0.76), Shutout (0.69), Infield_Put_Outs (0.67), Fielding Percentage (0.66), Doubles (0.66), At Bats (0.63), Walks (0.62), Strikeouts Allowed (0.62). But after checking the correlation between these variables, we eliminate:

• At_Bats has strong correlation with Hits (0.77) and Infield Put Out (0.92), Fielding Pencentage (0.72)
• Infield Put Outs has strong correlation with At Bat (0.92), Shutout (0.71), Strikeouts_Allowed (0.77), and Fielding_Percentage (0.85)
• Hits as strong correlation with At_Bats (0.76), Double (0.79), and Walk (0.69)
• Fielding Percentage has strong correlation with ShutOut (0.74) and Saves (0.75)

We then pick the next 4 variables that have high correlations with the dependent variable which are Runs_Scored (0.61), Saves (0.59), Triples (0.57), Home_Runs (0.72). After checking the correlation between these 4 variables with the first 4 varibles, we then eliminate Runs_Scored as it has high correlations with Triples (0.71) & Home_Runs (0.72).

Finally, we pick Complete_Games (0.37) to replace Runs_Scored, and it does not have high correlation with any other variables in the candidate list

Now we have the top 8 variables that do not have strong correlation with each other

• Offensive: Doubles (0.66), Tripples (0.56), Walks (0.62), Home_Runs (0.49)
• Defensive: Shutout (0.69), Strikeouts Allowed (0.62), Saves (0.59), Complete_Games (0.37)

From the look of the histograms, Saves, Shutout and Home_Runs are right skewed, Complete_Games is left skewed, we will remove these variables from the top 8

The final variables that have the highest correlation:

• Offensive: Doubles (0.66), Tripples (0.56), Walks (0.62)
• Defensive: Strikeouts Allowed (0.62)

Because there are 3 offensive variables and 1 defensive variables, the style of play for this period is Offensive

Checking Linear Relationship between Offensive and Defensive Variables with Games Won

Offensive Measurement

offensive = ['Doubles','Triples', 'Walks', 'Home_Runs']
for i in offensive:
    sns.scatterplot(data_baseball_1,x=i,y='Games_Won')
    plt.show()

The first 3 variables have strong linear relationship with Games Won. Home_Runs seems not to have a strong linear relationship with Games Won

Defensive Measurement

defensive = ['Shutout','Saves', 'Strikeouts_Allowed','Complete_Games']
for i in defensive:
    sns.scatterplot(data_baseball_1,x=i,y='Games_Won')
    plt.show()

All 4 variables have linear relationships with Games Won

data_baseball_1[['Doubles','Triples', 'Walks', 'Home_Runs', 'Shutout','Saves', 'Strikeouts_Allowed','Complete_Games']].hist(bins=20, figsize=(16,10))
plt.show()

---

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---

Section 3.2. Correlation Analysis of Period 2 - 1920 to 1959

df2=data_baseball[(data_baseball['Year']>1920) & (data_baseball['Year']<=1959)]
df2.head(5)

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
719	1921	BOS	BOS	5	154	75	79	668	5206	1440	...	5	4092	1521	53	452	446	157	151.0	0.97	Boston Red Sox
720	1921	BRO	LAD	5	152	77	75	667	5263	1476	...	12	4089	1556	46	361	471	232	142.0	0.96	Brooklyn Robins
721	1921	BSN	ATL	4	153	79	74	721	5385	1561	...	12	4155	1488	54	420	382	199	122.0	0.96	Boston Braves
722	1921	CHA	CHW	7	154	62	92	683	5329	1509	...	9	4095	1603	52	549	392	199	155.0	0.96	Chicago White Sox
723	1921	CHN	CHC	7	153	64	89	668	5321	1553	...	7	4089	1605	67	409	441	166	129.0	0.97	Chicago Cubs

5 rows × 31 columns

We will remove Strike_Outs Column as it does not have enough data for this period

data_baseball_2=df2.drop(['Franchise ','Final_Standing','Games_Played','Games_Lost', 'Strike_Outs'], axis='columns', inplace=False)
data_baseball_2.head()

	Year	Team	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
719	1921	BOS	75	668	5206	1440	248	69	17	428	...	5	4092	1521	53	452	446	157	151.0	0.97	Boston Red Sox
720	1921	BRO	77	667	5263	1476	209	85	59	325	...	12	4089	1556	46	361	471	232	142.0	0.96	Brooklyn Robins
721	1921	BSN	79	721	5385	1561	209	100	61	377	...	12	4155	1488	54	420	382	199	122.0	0.96	Boston Braves
722	1921	CHA	62	683	5329	1509	242	82	35	445	...	9	4095	1603	52	549	392	199	155.0	0.96	Chicago White Sox
723	1921	CHN	64	668	5321	1553	234	56	37	343	...	7	4089	1605	67	409	441	166	129.0	0.97	Chicago Cubs

5 rows × 26 columns

data_baseball_2.corr(method='spearman',numeric_only=True)

	Year	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	Stolen_Bases	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
Year	1.000000	0.003614	-0.286215	-0.244734	-0.626035	-0.537748	-0.646351	0.539521	0.374539	-0.520503	...	0.225234	0.523644	0.190051	-0.599826	0.664850	0.386546	0.732192	-0.701638	0.285147	0.555904
Games_Won	0.003614	1.000000	0.646088	0.244756	0.406018	0.242822	0.236794	0.337866	0.352178	0.165264	...	0.519055	0.400856	0.394018	-0.464102	-0.100038	-0.238954	0.344999	-0.329646	0.048373	0.312221
Runs_Scored	-0.286215	0.646088	1.000000	0.499992	0.784664	0.614051	0.458482	0.357141	0.403326	0.295935	...	-0.001616	0.180740	0.060217	0.151269	0.049497	-0.031496	0.042451	0.041555	0.020241	-0.073445
At_Bats	-0.244734	0.244756	0.499992	1.000000	0.694599	0.537271	0.305162	0.075031	-0.071665	0.103420	...	-0.059148	-0.042488	0.406688	0.293746	-0.047121	-0.085733	-0.020439	0.179172	-0.003322	-0.099794
Hits	-0.626035	0.406018	0.784664	0.694599	1.000000	0.751915	0.622882	-0.029016	-0.059981	0.390425	...	-0.127578	-0.112140	0.031054	0.438466	-0.247003	-0.257385	-0.271597	0.356765	-0.100321	-0.293233
Doubles	-0.537748	0.242822	0.614051	0.537271	0.751915	1.000000	0.495230	-0.108846	0.041819	0.336566	...	-0.174151	-0.158322	-0.037458	0.447412	-0.222693	-0.120245	-0.258685	0.339409	-0.099956	-0.280776
Triples	-0.646351	0.236794	0.458482	0.305162	0.622882	0.495230	1.000000	-0.309150	-0.086452	0.479116	...	-0.134950	-0.184666	-0.052955	0.370779	-0.414141	-0.240850	-0.364113	0.444178	-0.120395	-0.373057
Home_Runs	0.539521	0.337866	0.357141	0.075031	-0.029016	-0.108846	-0.309150	1.000000	0.370917	-0.335661	...	0.097738	0.512814	0.095705	-0.314916	0.690838	0.232331	0.622989	-0.494533	0.192360	0.344251
Walks	0.374539	0.352178	0.403326	-0.071665	-0.059981	0.041819	-0.086452	0.370917	1.000000	-0.052033	...	0.139975	0.357541	0.126279	-0.269716	0.291906	0.434837	0.367357	-0.368320	0.167018	0.270386
Stolen_Bases	-0.520503	0.165264	0.295935	0.103420	0.390425	0.336566	0.479116	-0.335661	-0.052033	1.000000	...	-0.050139	-0.186946	0.044268	0.239410	-0.372661	-0.183922	-0.303546	0.378207	-0.096533	-0.304591
Runs_Against	-0.302324	-0.615487	0.090931	0.166083	0.236514	0.298859	0.180093	-0.114021	-0.074796	0.079060	...	-0.740877	-0.301108	-0.426160	0.830230	0.177854	0.310423	-0.399037	0.489830	-0.022776	-0.474234
Earned_Runs	-0.156537	-0.602482	0.079347	0.140458	0.164270	0.243605	0.077195	-0.004446	-0.001954	0.000526	...	-0.717601	-0.221262	-0.408754	0.752064	0.312966	0.391139	-0.281659	0.322173	0.042096	-0.333654
Earned_Run_Average	-0.167747	-0.616380	0.068404	0.094835	0.153582	0.235603	0.078800	-0.016359	-0.016420	-0.005377	...	-0.721786	-0.234578	-0.484619	0.748579	0.301385	0.380743	-0.302801	0.330902	0.031486	-0.345943
Complete_Games	-0.577240	0.341673	0.258781	0.159468	0.387713	0.327732	0.420646	-0.343445	-0.103390	0.388276	...	0.206408	-0.513033	0.074903	0.065056	-0.563590	-0.399312	-0.372821	0.264284	-0.175052	-0.179839
Shutout	0.225234	0.519055	-0.001616	-0.059148	-0.127578	-0.174151	-0.134950	0.097738	0.139975	-0.050139	...	1.000000	0.205206	0.357931	-0.621933	-0.145910	-0.200622	0.333962	-0.408837	0.053920	0.373022
Saves	0.523644	0.400856	0.180740	-0.042488	-0.112140	-0.158322	-0.184666	0.512814	0.357541	-0.186946	...	0.205206	1.000000	0.219986	-0.438558	0.383228	0.177389	0.586044	-0.477646	0.199759	0.381824
Infield_Put_Outs	0.190051	0.394018	0.060217	0.406688	0.031054	-0.037458	-0.052955	0.095705	0.126279	0.044268	...	0.357931	0.219986	1.000000	-0.300374	-0.032738	-0.074637	0.335975	-0.229324	0.088070	0.272851
Hits_Allowed	-0.599826	-0.464102	0.151269	0.293746	0.438466	0.447412	0.370779	-0.314916	-0.269716	0.239410	...	-0.621933	-0.438558	-0.300374	1.000000	-0.140169	-0.091030	-0.620452	0.627175	-0.106445	-0.525222
Home_Run_Allowed	0.664850	-0.100038	0.049497	-0.047121	-0.247003	-0.222693	-0.414141	0.690838	0.291906	-0.372661	...	-0.145910	0.383228	-0.032738	-0.140169	1.000000	0.360044	0.517713	-0.457692	0.226421	0.290784
Walks_Allowed	0.386546	-0.238954	-0.031496	-0.085733	-0.257385	-0.120245	-0.240850	0.232331	0.434837	-0.183922	...	-0.200622	0.177389	-0.074637	-0.091030	0.360044	1.000000	0.270360	-0.188106	0.335863	0.082026
Strikeouts_Allowed	0.732192	0.344999	0.042451	-0.020439	-0.271597	-0.258685	-0.364113	0.622989	0.367357	-0.303546	...	0.333962	0.586044	0.335975	-0.620452	0.517713	0.270360	1.000000	-0.632651	0.109443	0.493691
Errors	-0.701638	-0.329646	0.041555	0.179172	0.356765	0.339409	0.444178	-0.494533	-0.368320	0.378207	...	-0.408837	-0.477646	-0.229324	0.627175	-0.457692	-0.188106	-0.632651	1.000000	-0.285144	-0.828624
Double_Plays	0.285147	0.048373	0.020241	-0.003322	-0.100321	-0.099956	-0.120395	0.192360	0.167018	-0.096533	...	0.053920	0.199759	0.088070	-0.106445	0.226421	0.335863	0.109443	-0.285144	1.000000	0.259383
Fielding_Percentage	0.555904	0.312221	-0.073445	-0.099794	-0.293233	-0.280776	-0.373057	0.344251	0.270386	-0.304591	...	0.373022	0.381824	0.272851	-0.525222	0.290784	0.082026	0.493691	-0.828624	0.259383	1.000000

24 rows × 24 columns

df2_corr=data_baseball_2.corr(method='spearman',numeric_only=True)
print((df2_corr['Games_Won'].sort_values(ascending=False)))

Games_Won              1.000000
Runs_Scored            0.646088
Shutout                0.519055
Hits                   0.406018
Saves                  0.400856
Infield_Put_Outs       0.394018
Walks                  0.352178
Strikeouts_Allowed     0.344999
Complete_Games         0.341673
Home_Runs              0.337866
Fielding_Percentage    0.312221
At_Bats                0.244756
Doubles                0.242822
Triples                0.236794
Stolen_Bases           0.165264
Double_Plays           0.048373
Year                   0.003614
Home_Run_Allowed      -0.100038
Walks_Allowed         -0.238954
Errors                -0.329646
Hits_Allowed          -0.464102
Earned_Runs           -0.602482
Runs_Against          -0.615487
Earned_Run_Average    -0.616380
Name: Games_Won, dtype: float64

Top 8 variables that have strong correlation with Games Won are : Earned_Runs (-0.60), Runs_Against (-0.62), and Earned_Run_Average (-0.62), Runs_Scored (0.65), Shutout (0.52), Hits (0.41), Hit_Allowed (-0.46)

Multicollinearity:

• Earned_Runs: high correlation with Earned_Run_Average (1) & Runs_Against (0.97), Hits_Allowed (0.75), Shut Out (-0.72)

After eliminating 3 variables above (Earned_Runs, Earned_Run_Average, Runs_Against) from the list, we then pick Hits (0.41), Saves (0.4), Infield_Put_Outs (0.39), Walks (0.35), Strikeouts_Allowed (0.34)

• Hit: has a high correlation with Run_Scored, so we then pick Complete_Games

Top 8 candidates:

• Offensive: Runs_Scored (0.65), Walks (0.35)
• Defensive: Shutout (0.52), Saves (0.4), Infield_Put_Outs (0.39), Hits_Allowed (-0.46), Strikeouts_Allowed (0.34), Complete_Games (0.34)

However, from the look of the histogram, we can see that Shutout, Saves and Strikeouts_Allowed are right skewed, so we'll remove these 3 from the top 8

The final top candidates:

• Offensive: Runs_Scored (0.65), Walks (0.35)
• Defensive: Infield_Put_Outs (0.39), Hits_Allowed (-0.46),Complete_Games (0.34)

The style of play for this Period is Defensive

Checking Linear Relationship between Top 4 Variables with Games Won

top8 = ['Runs_Scored', 'Walks','Shutout', 'Saves', 'Infield_Put_Outs', 'Hits_Allowed', 'Strikeouts_Allowed', 'Complete_Games' ]

for i in top8:
    sns.scatterplot(data_baseball_2,x=i,y='Games_Won')
    plt.show()

All 8 variables have linear relationship with Games Won

data_baseball_2[['Runs_Scored', 'Walks','Shutout', 'Saves', 'Infield_Put_Outs', 'Hits_Allowed', 'Strikeouts_Allowed', 'Complete_Games']].hist(bins=20, figsize=(16,10))
plt.show()

Section 3.3. Correlation Analysis of Period 3 - 1960 to 1989

df3=data_baseball[(data_baseball['Year']>=1960) & (data_baseball['Year']<=1989)]
df3.head(5)

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
1343	1960	BAL	BAL	2	154	89	65	682	5170	1307	...	22	4125	1222	117	552	785	107	172.0	0.98	Baltimore Orioles
1344	1960	BOS	BOS	7	154	65	89	658	5215	1359	...	23	4083	1440	127	580	767	140	156.0	0.97	Boston Red Sox
1345	1960	CHA	CHW	3	154	87	67	741	5191	1402	...	26	4143	1338	127	533	695	109	175.0	0.98	Chicago White Sox
1346	1960	CHN	CHC	7	156	60	94	634	5311	1293	...	25	4206	1393	152	565	805	143	133.0	0.97	Chicago Cubs
1347	1960	CIN	CIN	6	154	67	87	640	5289	1324	...	35	4170	1417	134	442	740	125	155.0	0.97	Cincinnati Reds

5 rows × 31 columns

data_baseball_3=df3.drop(['Franchise ','Final_Standing','Games_Played','Games_Lost'], axis='columns', inplace=False)
data_baseball_3.head()

	Year	Team	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
1343	1960	BAL	89	682	5170	1307	206	33	123	596	...	22	4125	1222	117	552	785	107	172.0	0.98	Baltimore Orioles
1344	1960	BOS	65	658	5215	1359	234	32	124	570	...	23	4083	1440	127	580	767	140	156.0	0.97	Boston Red Sox
1345	1960	CHA	87	741	5191	1402	242	38	112	567	...	26	4143	1338	127	533	695	109	175.0	0.98	Chicago White Sox
1346	1960	CHN	60	634	5311	1293	213	48	119	531	...	25	4206	1393	152	565	805	143	133.0	0.97	Chicago Cubs
1347	1960	CIN	67	640	5289	1324	230	40	140	512	...	35	4170	1417	134	442	740	125	155.0	0.97	Cincinnati Reds

5 rows × 27 columns

data_baseball_3.corr(method='spearman',numeric_only=True)

	Year	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	Strike_Outs	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
Year	1.000000	-0.029954	0.154436	0.156098	0.242286	0.452462	-0.144376	-0.016947	0.033468	-0.134195	...	-0.226960	0.287252	-0.017494	0.239870	-0.036910	0.023661	-0.118609	-0.238096	-0.030629	0.218578
Games_Won	-0.029954	1.000000	0.628775	0.352010	0.493893	0.355417	0.209896	0.412268	0.312605	0.022689	...	0.458363	0.481143	0.435602	-0.229717	-0.054089	-0.298456	0.252206	-0.213304	0.083860	0.233488
Runs_Scored	0.154436	0.628775	1.000000	0.611436	0.810858	0.655596	0.243196	0.687291	0.481312	-0.025570	...	-0.083663	0.370890	0.202812	0.335193	0.430790	0.075815	0.065151	-0.078533	0.243089	0.114494
At_Bats	0.156098	0.352010	0.611436	1.000000	0.812430	0.562374	0.285263	0.353044	0.085523	0.031112	...	-0.021389	0.237613	0.597540	0.422793	0.252931	0.103416	0.151501	0.082299	0.236492	0.029262
Hits	0.242286	0.493893	0.810858	0.812430	1.000000	0.711894	0.337892	0.386281	0.164012	-0.214934	...	-0.047773	0.311167	0.273947	0.427227	0.248137	0.060071	-0.007018	-0.004355	0.286569	0.068733
Doubles	0.452462	0.355417	0.655596	0.562374	0.711894	1.000000	0.284817	0.336022	0.182651	-0.049827	...	-0.094101	0.366483	0.160835	0.387455	0.234213	0.112794	0.030630	-0.081352	0.182083	0.124019
Triples	-0.144376	0.209896	0.243196	0.285263	0.337892	0.284817	1.000000	-0.071509	-0.029809	0.021917	...	0.050174	0.090665	0.147100	0.123128	-0.007936	-0.006610	-0.021619	0.128806	0.110123	-0.071509
Home_Runs	-0.016947	0.412268	0.687291	0.353044	0.386281	0.336022	-0.071509	1.000000	0.349417	0.263787	...	-0.102523	0.269982	0.081249	0.217285	0.588692	0.088878	0.198703	-0.088802	0.136797	0.126191
Walks	0.033468	0.312605	0.481312	0.085523	0.164012	0.182651	-0.029809	0.349417	1.000000	0.143155	...	-0.049912	0.128970	0.175078	0.204290	0.272592	0.221483	0.117903	0.009953	0.148122	0.051578
Strike_Outs	-0.134195	0.022689	-0.025570	0.031112	-0.214934	-0.049827	0.021917	0.263787	0.143155	1.000000	...	0.061687	0.165886	0.214791	-0.041198	0.211949	0.187549	0.466592	0.149596	-0.031628	-0.038730
Stolen_Bases	0.530798	0.182627	0.171012	0.121200	0.217381	0.327068	0.152363	-0.154718	0.151028	-0.003202	...	-0.009799	0.264422	0.212512	0.050405	-0.139751	0.042666	-0.035594	-0.025078	-0.057478	0.040451
Runs_Against	0.170104	-0.393825	0.299163	0.302378	0.307657	0.322691	0.066245	0.287172	0.221993	0.075442	...	-0.595011	-0.062678	-0.152622	0.831224	0.669774	0.582940	-0.110281	0.321539	0.254893	-0.197592
Earned_Runs	0.207108	-0.358201	0.330691	0.319761	0.334683	0.360182	0.063310	0.312797	0.231876	0.064893	...	-0.598940	-0.029873	-0.149418	0.831591	0.695448	0.566545	-0.110451	0.211893	0.266836	-0.112742
Earned_Run_Average	0.226628	-0.483987	0.232658	0.169822	0.225245	0.264171	-0.002305	0.236369	0.134042	-0.041424	...	-0.684679	-0.114241	-0.339867	0.751748	0.635865	0.494677	-0.229263	0.130949	0.184900	-0.119452
Complete_Games	-0.542194	0.298612	0.069532	0.013862	0.046969	-0.170531	0.101545	0.077548	0.067852	-0.114150	...	0.448311	-0.472783	0.111350	-0.184202	-0.080215	-0.162110	0.050935	0.082085	0.065949	-0.046324
Shutout	-0.226960	0.458363	-0.083663	-0.021389	-0.047773	-0.094101	0.050174	-0.102523	-0.049912	0.061687	...	1.000000	0.018652	0.303477	-0.473136	-0.413671	-0.311853	0.251257	-0.071790	-0.032082	0.112544
Saves	0.287252	0.481143	0.370890	0.237613	0.311167	0.366483	0.090665	0.269982	0.128970	0.165886	...	0.018652	1.000000	0.218254	-0.016984	0.086123	-0.046638	0.208578	-0.157064	0.047909	0.167216
Infield_Put_Outs	-0.017494	0.435602	0.202812	0.597540	0.273947	0.160835	0.147100	0.081249	0.175078	0.214791	...	0.303477	0.218254	1.000000	0.013079	-0.090857	-0.023655	0.352814	0.091700	0.072292	0.061301
Hits_Allowed	0.239870	-0.229717	0.335193	0.422793	0.427227	0.387455	0.123128	0.217285	0.204290	-0.041198	...	-0.473136	-0.016984	0.013079	1.000000	0.464405	0.275620	-0.242255	0.300674	0.344285	-0.132303
Home_Run_Allowed	-0.036910	-0.054089	0.430790	0.252931	0.248137	0.234213	-0.007936	0.588692	0.272592	0.211949	...	-0.413671	0.086123	-0.090857	0.464405	1.000000	0.332911	0.079159	0.025220	0.170257	0.011785
Walks_Allowed	0.023661	-0.298456	0.075815	0.103416	0.060071	0.112794	-0.006610	0.088878	0.221483	0.187549	...	-0.311853	-0.046638	-0.023655	0.275620	0.332911	1.000000	0.122814	0.228565	0.232633	-0.171252
Strikeouts_Allowed	-0.118609	0.252206	0.065151	0.151501	-0.007018	0.030630	-0.021619	0.198703	0.117903	0.466592	...	0.251257	0.208578	0.352814	-0.242255	0.079159	0.122814	1.000000	0.018221	-0.252862	0.005303
Errors	-0.238096	-0.213304	-0.078533	0.082299	-0.004355	-0.081352	0.128806	-0.088802	0.009953	0.149596	...	-0.071790	-0.157064	0.091700	0.300674	0.025220	0.228565	0.018221	1.000000	0.064740	-0.767833
Double_Plays	-0.030629	0.083860	0.243089	0.236492	0.286569	0.182083	0.110123	0.136797	0.148122	-0.031628	...	-0.032082	0.047909	0.072292	0.344285	0.170257	0.232633	-0.252862	0.064740	1.000000	0.039074
Fielding_Percentage	0.218578	0.233488	0.114494	0.029262	0.068733	0.124019	-0.071509	0.126191	0.051578	-0.038730	...	0.112544	0.167216	0.061301	-0.132303	0.011785	-0.171252	0.005303	-0.767833	0.039074	1.000000

25 rows × 25 columns

df3_corr = data_baseball_3.corr(method='spearman',numeric_only=True)
print(df3_corr['Games_Won'].sort_values(ascending=False))

Games_Won              1.000000
Runs_Scored            0.628775
Hits                   0.493893
Saves                  0.481143
Shutout                0.458363
Infield_Put_Outs       0.435602
Home_Runs              0.412268
Doubles                0.355417
At_Bats                0.352010
Walks                  0.312605
Complete_Games         0.298612
Strikeouts_Allowed     0.252206
Fielding_Percentage    0.233488
Triples                0.209896
Stolen_Bases           0.182627
Double_Plays           0.083860
Strike_Outs            0.022689
Year                  -0.029954
Home_Run_Allowed      -0.054089
Errors                -0.213304
Hits_Allowed          -0.229717
Walks_Allowed         -0.298456
Earned_Runs           -0.358201
Runs_Against          -0.393825
Earned_Run_Average    -0.483987
Name: Games_Won, dtype: float64

Top 8 variables that have the highest correlation with Games Won are Runs_Scored (0.63), Hits (0.49), Saves (0.48), Earned_Run_Average (-0.48), Shutout (0.46), Infield_Put_Out (0.44), Home_Runs (0.41), Runs_Against (0.39). But after checking the correlation between these variables, we eliminate:

• Runs_Against: strong correlation with Earned_Run_Average (0.98)
• Hit: strong correlation with Run_Scored (0.98)

We then pick the next 2 variables that have high correlations with the dependent variable which are Doubles (0.36) and At_Bats (0.35). These 2 variables do not have high correlation with any other variables in the candidate list

Top 8 variables that have strong correlation with Games Won are :

• Offensive: Runs_Scored (0.63), Home_Runs (0.41), Doubles (0.36), At_Bats (0.35)
• Defensive: Earned_Run_Average (-0.48), Shutout (0.46), Saves (0.48), Infield_Put_Outs (0.44)

However, At_Bats and Infield_Put_Outs do not have a linear relationship with Games Won (according the the scatter matrixes below), and Shutout and Saves' histograms do not have a symmetric share. So we'll remove these 4 varibles from top 8

Top FINAL variables that have strong correlation with Games Won are :

• Offensive: Runs_Scored (0.63), Home_Runs (0.41), Doubles (0.36)
• Defensive: Earned_Run_Average (-0.48)

The style of play for this Period is Offensive

Checking Linear Relationship between Top 8 Variables with Games Won

top_p3 = ['Runs_Scored','Home_Runs','Doubles','At_Bats','Saves','Earned_Run_Average','Shutout','Infield_Put_Outs']

for i in top_p3:
    sns.scatterplot(data_baseball_3,x=i,y='Games_Won')
    plt.show()

All variables have linear relationship with Games Won except At_Bats and Infield_Put_Outs

data_baseball_3[['Runs_Scored','Home_Runs','Doubles','At_Bats','Saves','Earned_Run_Average','Shutout','Infield_Put_Outs']].hist(bins=20, figsize=(16,10))
plt.show()

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Section 3.4. Correlation Analysis of Period 4 - 1990 to 2010

df4=data_baseball[(data_baseball['Year']>=1990) & (data_baseball['Year']<=2010)]
df4.head(5)

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
2047	1990	ATL	ATL	6	162	65	97	682	5504	1376	...	30	4287	1527	128	579	938	158	133.0	0.97	Atlanta Braves
2048	1990	BAL	BAL	5	161	76	85	669	5410	1328	...	43	4305	1445	161	537	776	91	151.0	0.98	Baltimore Orioles
2049	1990	BOS	BOS	1	162	88	74	699	5516	1502	...	44	4326	1439	92	519	997	123	154.0	0.98	Boston Red Sox
2050	1990	CAL	ANA	4	162	80	82	690	5570	1448	...	42	4362	1482	106	544	944	140	186.0	0.97	California Angels
2051	1990	CHA	CHW	2	162	94	68	682	5402	1393	...	68	4347	1313	106	548	914	124	169.0	0.98	Chicago White Sox

5 rows × 31 columns

data_baseball_4=df4.drop(['Franchise ','Final_Standing','Games_Played','Games_Lost'], axis='columns', inplace=False)

data_baseball_4.head()

	Year	Team	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
2047	1990	ATL	65	682	5504	1376	263	26	162	473	...	30	4287	1527	128	579	938	158	133.0	0.97	Atlanta Braves
2048	1990	BAL	76	669	5410	1328	234	22	132	660	...	43	4305	1445	161	537	776	91	151.0	0.98	Baltimore Orioles
2049	1990	BOS	88	699	5516	1502	298	31	106	598	...	44	4326	1439	92	519	997	123	154.0	0.98	Boston Red Sox
2050	1990	CAL	80	690	5570	1448	237	27	147	566	...	42	4362	1482	106	544	944	140	186.0	0.97	California Angels
2051	1990	CHA	94	682	5402	1393	251	44	106	478	...	68	4347	1313	106	548	914	124	169.0	0.98	Chicago White Sox

5 rows × 27 columns

data_baseball_4.corr(method='spearman',numeric_only=True)

	Year	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	Strike_Outs	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
Year	1.000000	0.117956	0.223444	0.256397	0.235970	0.480090	-0.052715	0.322269	0.058329	0.497652	...	0.079600	0.002486	0.052886	0.222745	0.387507	0.051609	0.515073	-0.307064	0.166983	0.674834
Games_Won	0.117956	1.000000	0.600772	0.298512	0.461585	0.339706	0.035645	0.426131	0.507042	0.052432	...	0.507288	0.684815	0.554787	-0.238813	-0.149116	-0.214491	0.453809	-0.180135	-0.013667	0.312278
Runs_Scored	0.223444	0.600772	1.000000	0.673056	0.803931	0.619613	0.033000	0.764597	0.609977	0.200393	...	0.007605	0.261026	0.238576	0.362677	0.418509	0.142702	0.277957	-0.046926	0.217805	0.223405
At_Bats	0.256397	0.298512	0.673056	1.000000	0.874977	0.594066	0.094263	0.457170	0.258118	0.162638	...	-0.032167	0.124826	0.449639	0.523387	0.421662	0.237404	0.235969	0.003482	0.298820	0.231437
Hits	0.235970	0.461585	0.803931	0.874977	1.000000	0.640528	0.132141	0.483970	0.321615	0.028714	...	0.017088	0.223530	0.291060	0.452449	0.399882	0.165526	0.246038	-0.042426	0.269213	0.246081
Doubles	0.480090	0.339706	0.619613	0.594066	0.640528	1.000000	0.065931	0.464299	0.303788	0.310375	...	0.061033	0.115909	0.187431	0.342565	0.369003	0.142777	0.380712	-0.090420	0.220698	0.377380
Triples	-0.052715	0.035645	0.033000	0.094263	0.132141	0.065931	1.000000	-0.164444	-0.088981	0.004636	...	0.056934	0.067381	0.066655	0.044319	0.004001	0.050013	-0.034742	0.053635	0.008206	-0.014156
Home_Runs	0.322269	0.426131	0.764597	0.457170	0.483970	0.464299	-0.164444	1.000000	0.459200	0.398992	...	-0.043797	0.180270	0.148960	0.290357	0.446190	0.175666	0.327087	-0.057283	0.171135	0.248714
Walks	0.058329	0.507042	0.609977	0.258118	0.321615	0.303788	-0.088981	0.459200	1.000000	0.283824	...	0.101953	0.243844	0.327108	0.122227	0.152545	0.164598	0.282681	0.009993	0.119820	0.087310
Strike_Outs	0.497652	0.052432	0.200393	0.162638	0.028714	0.310375	0.004636	0.398992	0.283824	1.000000	...	0.011215	0.007178	0.161116	0.273001	0.350987	0.258911	0.434378	0.120098	0.143034	0.190811
Stolen_Bases	-0.235142	0.127314	0.006765	-0.050920	0.012280	-0.168362	0.209106	-0.177638	0.014833	-0.079186	...	0.089870	0.153227	0.156520	-0.060393	-0.058808	-0.011643	-0.001613	0.157228	-0.105856	-0.203871
Runs_Against	0.208688	-0.380634	0.336086	0.442486	0.371873	0.322748	0.024142	0.334318	0.120164	0.315951	...	-0.471475	-0.292816	-0.200913	0.873788	0.745458	0.564842	-0.080155	0.303241	0.366978	-0.074135
Earned_Runs	0.257822	-0.351739	0.360851	0.461868	0.398964	0.348836	0.024992	0.356028	0.130781	0.317202	...	-0.462647	-0.278017	-0.191966	0.869671	0.773979	0.556827	-0.062359	0.198534	0.372593	0.014360
Earned_Run_Average	0.133612	-0.553397	0.195758	0.241618	0.197874	0.170389	-0.048430	0.234893	-0.024736	0.137474	...	-0.628254	-0.456560	-0.457021	0.705535	0.667019	0.434150	-0.266576	0.089091	0.223443	-0.084416
Complete_Games	-0.599190	0.068889	-0.108591	-0.176729	-0.143907	-0.268171	0.026889	-0.198182	0.023349	-0.351041	...	0.205699	-0.070588	0.049852	-0.219996	-0.320861	-0.142088	-0.254914	0.133735	-0.057114	-0.365955
Shutout	0.079600	0.507288	0.007605	-0.032167	0.017088	0.061033	0.056934	-0.043797	0.101953	0.011215	...	1.000000	0.375344	0.378517	-0.358188	-0.345941	-0.213151	0.341663	-0.097060	-0.008776	0.217200
Saves	0.002486	0.684815	0.261026	0.124826	0.223530	0.115909	0.067381	0.180270	0.243844	0.007178	...	0.375344	1.000000	0.456024	-0.165830	-0.152615	-0.142756	0.271737	-0.036862	-0.047768	0.149132
Infield_Put_Outs	0.052886	0.554787	0.238576	0.449639	0.291060	0.187431	0.066655	0.148960	0.327108	0.161116	...	0.378517	0.456024	1.000000	-0.032067	-0.095983	0.001279	0.387216	0.007927	0.100881	0.194005
Hits_Allowed	0.222745	-0.238813	0.362677	0.523387	0.452449	0.342565	0.044319	0.290357	0.122227	0.273001	...	-0.358188	-0.165830	-0.032067	1.000000	0.638502	0.332399	-0.118659	0.264807	0.463829	-0.005140
Home_Run_Allowed	0.387507	-0.149116	0.418509	0.421662	0.399882	0.369003	0.004001	0.446190	0.152545	0.350987	...	-0.345941	-0.152615	-0.095983	0.638502	1.000000	0.319042	0.111271	0.021363	0.234086	0.195984
Walks_Allowed	0.051609	-0.214491	0.142702	0.237404	0.165526	0.142777	0.050013	0.175666	0.164598	0.258911	...	-0.213151	-0.142756	0.001279	0.332399	0.319042	1.000000	0.097742	0.261717	0.321311	-0.104418
Strikeouts_Allowed	0.515073	0.453809	0.277957	0.235969	0.246038	0.380712	-0.034742	0.327087	0.282681	0.434378	...	0.341663	0.271737	0.387216	-0.118659	0.111271	0.097742	1.000000	-0.090884	-0.124430	0.372185
Errors	-0.307064	-0.180135	-0.046926	0.003482	-0.042426	-0.090420	0.053635	-0.057283	0.009993	0.120098	...	-0.097060	-0.036862	0.007927	0.264807	0.021363	0.261717	-0.090884	1.000000	0.069721	-0.733841
Double_Plays	0.166983	-0.013667	0.217805	0.298820	0.269213	0.220698	0.008206	0.171135	0.119820	0.143034	...	-0.008776	-0.047768	0.100881	0.463829	0.234086	0.321311	-0.124430	0.069721	1.000000	0.143587
Fielding_Percentage	0.674834	0.312278	0.223405	0.231437	0.246081	0.377380	-0.014156	0.248714	0.087310	0.190811	...	0.217200	0.149132	0.194005	-0.005140	0.195984	-0.104418	0.372185	-0.733841	0.143587	1.000000

25 rows × 25 columns

df4_corr=data_baseball_4.corr(method='spearman',numeric_only=True)
print(df4_corr['Games_Won'].sort_values(ascending=False))

Games_Won              1.000000
Saves                  0.684815
Runs_Scored            0.600772
Infield_Put_Outs       0.554787
Shutout                0.507288
Walks                  0.507042
Hits                   0.461585
Strikeouts_Allowed     0.453809
Home_Runs              0.426131
Doubles                0.339706
Fielding_Percentage    0.312278
At_Bats                0.298512
Stolen_Bases           0.127314
Year                   0.117956
Complete_Games         0.068889
Strike_Outs            0.052432
Triples                0.035645
Double_Plays          -0.013667
Home_Run_Allowed      -0.149116
Errors                -0.180135
Walks_Allowed         -0.214491
Hits_Allowed          -0.238813
Earned_Runs           -0.351739
Runs_Against          -0.380634
Earned_Run_Average    -0.553397
Name: Games_Won, dtype: float64

Top 8 variables that have the highest correlation with Games Won are Earned_Run_Average (-0.55), Saves (0.68), Runs_Scored (0.60), Infield_Put_Outs (0.55), Shutout (0.50), Walks (0.50), Hits (0.46), Strikeouts Allowed (0.45).

After checking the normality and linear relationship (qq plot and scatter plot), we remove Infield_Put_Outs as it not normally distributed and does not have a linear relationship with Games Won. The next candidate could have been Home_Runs but it has a strong correlation with Runs_Score (0.76), so Doubles would be the last candidate.

The final 8 variables that have the highest correlation after considering their correlation with each other are

• Offensive: Runs Scored (0.60), Earned_Run_Average (-0.55), Walks (0.50), Hits (0.46), Doubles (0.34)
• Defensive: Shutout (0.50), Strikeouts Allowed (0.45), Saves (0.68)

All 8 candidate variables are not dependent of each other. Because there are 4 defensive variables out of 8, the style of play for this period is Balanced

Checking Linear Relationship between Offensive and Defensive Variables with Games Won

candidate = ['Earned_Run_Average', 'Shutout', 'Saves','Infield_Put_Outs','Strikeouts_Allowed', 'Walks','Runs_Scored','Hits','Strikeouts_Allowed','Doubles']
for i in candidate:
    sns.scatterplot(data_baseball_4,x=i,y='Games_Won')
    plt.show()

Even though Infield_Put_Outs seems to have a moderate relationship with Games Won, when we do a scatterplot to check the linear relationship, these 2 variables do not have a linear relationship visually. We might need to eliminate it from the candidate list to build the model

Checking Normality of top 8 candidate variables

candidate = ['Earned_Run_Average', 'Shutout', 'Saves', 'Infield_Put_Outs','Strikeouts_Allowed', 'Walks','Runs_Scored','Hits','Strikeouts_Allowed','Doubles']
for i in candidate:
    qqplot(data_baseball_4[i],line='s')
    plt.title(label=i)

All the independent variables have normal distribution (or close to normal distribution) except Infield_Put_Outs

Histogram Plots for each of the top 8 variables

data_baseball_4.describe()

	Year	Games_Won	Runs_Scored	At_Bats	Hits	Doubles	Triples	Home_Runs	Walks	Strike_Outs	...	Shutout	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage
count	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	...	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000	608.000000
mean	2000.259868	79.445724	747.483553	5446.587171	1441.445724	280.891447	30.838816	161.365132	536.782895	1017.419408	...	8.276316	40.047697	4254.504934	1441.442434	161.365132	536.781250	1017.412829	108.421053	148.613487	0.980138
std	5.994086	12.282923	93.733980	363.314246	117.725690	35.682677	8.829355	37.691082	78.410122	136.028295	...	3.856909	7.784962	283.179215	124.154087	30.538358	73.369502	135.513189	18.933518	20.410780	0.004776
min	1990.000000	43.000000	466.000000	3856.000000	963.000000	159.000000	11.000000	68.000000	319.000000	568.000000	...	0.000000	20.000000	2952.000000	929.000000	76.000000	288.000000	560.000000	57.000000	82.000000	0.970000
25%	1995.000000	71.000000	686.000000	5478.750000	1398.000000	262.750000	24.000000	135.000000	486.750000	928.000000	...	6.000000	35.000000	4300.000000	1385.000000	141.000000	489.000000	935.500000	95.000000	135.000000	0.980000
50%	2000.000000	79.500000	747.000000	5533.500000	1452.500000	284.000000	30.000000	160.500000	533.000000	1028.000000	...	8.000000	40.000000	4328.000000	1452.000000	162.000000	537.500000	1021.000000	107.000000	149.000000	0.980000
75%	2005.000000	88.000000	807.000000	5601.000000	1510.250000	304.000000	36.250000	187.000000	589.250000	1105.250000	...	11.000000	45.000000	4358.000000	1521.250000	182.000000	582.000000	1106.250000	122.000000	162.000000	0.983000
max	2010.000000	116.000000	1009.000000	5781.000000	1684.000000	376.000000	61.000000	264.000000	775.000000	1529.000000	...	24.000000	68.000000	4467.000000	1734.000000	241.000000	784.000000	1404.000000	173.000000	204.000000	0.989000

8 rows × 25 columns

data_baseball_4[['Earned_Run_Average', 'Shutout', 'Saves','Strikeouts_Allowed', 'Walks','Runs_Scored','Hits','Doubles']].hist(bins=20, figsize=(16,10))
plt.show()

Modes of top 8 variables

data_baseball_4[['Earned_Run_Average', 'Shutout', 'Saves','Walks','Runs_Scored','Hits','Strikeouts_Allowed','Doubles']].mode()

	Earned_Run_Average	Shutout	Saves	Walks	Runs_Scored	Hits	Strikeouts_Allowed	Doubles
0	3.87	8.0	42.0	500	747.0	1408.0	997.0	294.0
1	4.13	NaN	NaN	511	772.0	NaN	NaN	NaN
2	4.21	NaN	NaN	519	NaN	NaN	NaN	NaN
3	4.23	NaN	NaN	526	NaN	NaN	NaN	NaN
4	NaN	NaN	NaN	536	NaN	NaN	NaN	NaN

Variance of top 8 variables

data_baseball_4[['Earned_Run_Average', 'Shutout', 'Saves','Walks','Runs_Scored','Doubles','Hits','Strikeouts_Allowed']].var(axis=0)

Earned_Run_Average        0.299431
Shutout                  14.875748
Saves                    60.605629
Walks                  6148.147186
Runs_Scored            8786.059037
Doubles                1273.253436
Hits                  13859.338071
Strikeouts_Allowed    18363.824349
dtype: float64

Comment on the histogram plots:

• Is it symmetric? yes, all shapes of the histogram plots for the top 8 variables are symmetric
• Is there a single mode? Shutout, Saves, Hits, Strikeouts_Allowed, and Doubles have a single mode. Earned_Run_Average, Runs_Scored, Walks have more than 1 mode. All the modes of the variables that have multiple modes have close values, that makes the top of histogram for those variables flatter than the ones that only have 1 single mode
• Is it narrow or wide? from the histogram plots and variance calculation, we can see that Earned_Run_Average, Shutout, and Saves have narrower histogram plots than the rest of top 8 variables. Hits seems to have a big variance, but from the look of the histogram plot, it can be from the outliers

Box Plots for each of the top 8 variables

candidate2 = ['Earned_Run_Average', 'Shutout', 'Saves','Walks','Runs_Scored','Hits','Strikeouts_Allowed','Doubles']
for i in candidate2:
    plt.boxplot(data_baseball_4[i])
    plt.title(label=i)
    plt.figure(figsize=(1,1))
    plt.show()

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

<Figure size 100x100 with 0 Axes>

Comment on the box plots:

Are there many outliers? yes, all 8 variables have outliers, however, Earned_Run_Average seems to be the variable that has the least outliers out of 8 variables

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Section 3.5 Summary - Style of Play by Period

Period	# of candidate variables	# of Offensive Measurement	# of Offensive Measurement	Style of Play
Period 1	7	4	3	Offensive
Period 2	4	1	3	Defensive
Period 3	4	3	1	Offensive
Period 4	7	3	4	Balanced

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Section 4 – Linear Regression Models

Section 4.1 Linear Regression Model for Period 4

x = data_baseball_4[['Year','Games_Won','Earned_Run_Average', 'Shutout', 'Saves', 'Strikeouts_Allowed', 'Walks', 'Runs_Scored', 'Hits', 'Doubles']]
y = data_baseball_4['Games_Won']

x_train, x_test, y_train, y_test = train_test_split(x, y, train_size=0.7, random_state=1)

x_train.corr(method='spearman')

	Year	Games_Won	Earned_Run_Average	Shutout	Saves	Strikeouts_Allowed	Walks	Runs_Scored	Hits	Doubles
Year	1.000000	0.117416	0.108228	0.076916	0.040540	0.499671	0.029491	0.187975	0.223441	0.457771
Games_Won	0.117416	1.000000	-0.536063	0.506401	0.694183	0.446054	0.501467	0.618414	0.493718	0.344472
Earned_Run_Average	0.108228	-0.536063	1.000000	-0.614966	-0.446337	-0.305579	0.000537	0.190898	0.177012	0.151402
Shutout	0.076916	0.506401	-0.614966	1.000000	0.390981	0.374718	0.051362	0.006828	0.038098	0.063106
Saves	0.040540	0.694183	-0.446337	0.390981	1.000000	0.282102	0.244940	0.284601	0.230298	0.137051
Strikeouts_Allowed	0.499671	0.446054	-0.305579	0.374718	0.282102	1.000000	0.235478	0.239279	0.232723	0.383407
Walks	0.029491	0.501467	0.000537	0.051362	0.244940	0.235478	1.000000	0.627916	0.351331	0.286358
Runs_Scored	0.187975	0.618414	0.190898	0.006828	0.284601	0.239279	0.627916	1.000000	0.804903	0.597991
Hits	0.223441	0.493718	0.177012	0.038098	0.230298	0.232723	0.351331	0.804903	1.000000	0.649448
Doubles	0.457771	0.344472	0.151402	0.063106	0.137051	0.383407	0.286358	0.597991	0.649448	1.000000

x_train_corr=x_train.corr(method='spearman')
print ((x_train_corr['Games_Won']).sort_values(ascending=False))

Games_Won             1.000000
Saves                 0.694183
Runs_Scored           0.618414
Shutout               0.506401
Walks                 0.501467
Hits                  0.493718
Strikeouts_Allowed    0.446054
Doubles               0.344472
Year                  0.117416
Earned_Run_Average   -0.536063
Name: Games_Won, dtype: float64

Build the model with a single independent: Saves

lm1 = smf.ols(formula='Games_Won ~ Saves',data = x_train).fit()
lm1.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.505
Model:	OLS	Adj. R-squared:	0.504
Method:	Least Squares	F-statistic:	431.5
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	1.41e-66
Time:	20:47:10	Log-Likelihood:	-1523.4
No. Observations:	425	AIC:	3051.
Df Residuals:	423	BIC:	3059.
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	33.9552	2.222	15.279	0.000	29.587	38.323
Saves	1.1349	0.055	20.773	0.000	1.028	1.242

Omnibus:	4.195	Durbin-Watson:	1.966
Prob(Omnibus):	0.123	Jarque-Bera (JB):	3.672
Skew:	0.150	Prob(JB):	0.159
Kurtosis:	2.657	Cond. No.	213.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

• R-square = 0.505 which means 50.5% variability in Games Won explained by the variability in Saves. This is not bad but we could improve it
• p-value of F-statistic = 1.41e-66 is very small (and smaller than 0.05) so we can reject the null hypothesis that there is no linear relationship between Saves and Games Won
• p-value of t-test is 0 which is smaller than 0.05 so we can reject the null hypothesis that Beta1 (Saves) is 0
• coef of Saves: 1.13 this means there is a positive relationship between Saves and Games Won and if Saves is held constant, then Games Won is expected to increase by 1.1349 for each additional unit of Saves

Conclusion: we will keep Saves in the model and add 1 more independent variable to see if the model is stronger

Build the model with 2 independents: Saves and Runs_Scored

lm2 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored',data = x_train).fit()
lm2.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.714
Model:	OLS	Adj. R-squared:	0.713
Method:	Least Squares	F-statistic:	527.5
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	1.57e-115
Time:	20:47:11	Log-Likelihood:	-1406.6
No. Observations:	425	AIC:	2819.
Df Residuals:	422	BIC:	2831.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	-3.2963	2.710	-1.216	0.225	-8.623	2.031
Saves	0.9075	0.044	20.852	0.000	0.822	0.993
Runs_Scored	0.0617	0.004	17.584	0.000	0.055	0.069

Omnibus:	15.765	Durbin-Watson:	2.104
Prob(Omnibus):	0.000	Jarque-Bera (JB):	16.599
Skew:	0.444	Prob(JB):	0.000249
Kurtosis:	3.384	Cond. No.	6.37e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 6.37e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

• Both R-squared R-squared Adjusted increased = 0.71 which means 71.3% variability in Games Won explained by the variability in Saves and Runs_Scored. This also means that adding Runs_Score does not make the model worse
• p-value of F-statistic = 1.57e-115 is very small (and smaller than 0.05) so we can reject the null hypothesis that there is no linear relationship between the independent variables (Saves and Runs_Scored) and Games Won
• p-value of t-test for Saves and Runs_Scored 0 which is smaller than 0.05 so we can reject the null hypothesis that Beta1 (Saves) and Beta2 (Runs_Scored) = 0 and there are no linear relationship between these 2 variables with Games Won
• The intercept of the model is not significant based on the p-value is 0.225 (>0.05), we will supress the intercep in the next model
• coef of Saves: 0.9 this means there is a positive relationship between Saves and Games Won and if Saves is held constant, then Games Won is expected to increase by 1.1349 for each additional unit of Saves
• coef of Runs_Scored: 0.06 this means there is a positive relationship between Runs Scored and Games Won and if Runs Scored is held constant, then Games Won is expected to increase by 0.06 for each additional unit of Runs Scored

Conclusion: We will try to supress the intercept to see if the model is better or worse

Build the model with 2 independents: Saves and Runs_Scored but supress the intercept

lm3 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored - 1',data = x_train).fit()
lm3.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared (uncentered):	0.993
Model:	OLS	Adj. R-squared (uncentered):	0.993
Method:	Least Squares	F-statistic:	3.072e+04
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	0.00
Time:	20:47:12	Log-Likelihood:	-1407.3
No. Observations:	425	AIC:	2819.
Df Residuals:	423	BIC:	2827.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Saves	0.8888	0.041	21.811	0.000	0.809	0.969
Runs_Scored	0.0584	0.002	26.654	0.000	0.054	0.063

Omnibus:	14.798	Durbin-Watson:	2.098
Prob(Omnibus):	0.001	Jarque-Bera (JB):	15.403
Skew:	0.436	Prob(JB):	0.000452
Kurtosis:	3.333	Cond. No.	95.9

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.

• Both R-squared R-squared Adjusted increased = 0.993 which means 99.3% variability in Games Won explained by the variability in Saves and Runs_Scored. This also means that adding Runs_Score does not make the model worse
• p-value of F-statistic = 0 is smaller than 0.05 so we can reject the null hypothesis that there is no linear relationship between the independent variables (Saves and Runs_Scored) and Games Won
• p-values of t-test for Savesand Runs_Scored are 0 which is smaller than 0.05 so we can reject the null hypothesis that Beta1 (Saves) and Beta2 (Runs_Scored) = 0 and there are no linear relationship between these 2 variables with Games Won
• coef of Saves: 0.88 this means there is a positive relationship between Saves and Games Won and if Saves is held constant, then Games Won is expected to increase by 1.1349 for each additional unit of Saves
• coef of Runs_Scored: 0.06 this means there is a positive relationship between Runs Scored and Games Won and if Runs Scored is held constant, then Games Won is expected to increase by 0.06 for each additional unit of Runs Scored

Conclusion: We will try to add another independent vairable to the model and add intercept back to the model to see if it gets better

Build the model with 3 independents: Saves and Runs_Scored, Earned_Run_Average

lm4 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored + Earned_Run_Average',data = x_train).fit()
lm4.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.922
Model:	OLS	Adj. R-squared:	0.921
Method:	Least Squares	F-statistic:	1650.
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	2.84e-232
Time:	20:47:13	Log-Likelihood:	-1131.8
No. Observations:	425	AIC:	2272.
Df Residuals:	421	BIC:	2288.
Df Model:	3
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	52.5169	2.195	23.923	0.000	48.202	56.832
Saves	0.4096	0.027	15.020	0.000	0.356	0.463
Runs_Scored	0.0877	0.002	43.881	0.000	0.084	0.092
Earned_Run_Average	-12.6762	0.380	-33.364	0.000	-13.423	-11.929

Omnibus:	1.451	Durbin-Watson:	1.987
Prob(Omnibus):	0.484	Jarque-Bera (JB):	1.424
Skew:	0.141	Prob(JB):	0.491
Kurtosis:	2.975	Cond. No.	9.93e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 9.93e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

• Both R-squared R-squared Adjusted decreased by a little bit. They are now 0.922 which means 92.2% variability in Games Won explained by the variability in Saves and Runs_Scored, Earned_Run_Average. This also means that adding Earned_Run_Average does not make the model worse
• p-value of F-statistic = 2.84e-232 is smaller than 0.05 so we can reject the null hypothesis that there is no linear relationship between the independent variables (Saves and Runs_Scored, Earned_Run_Average) and Games Won
• p-values of t-tests for Saves and Runs_Scored, and Earn_Run_Average are 0 which is smaller than 0.05 so we can reject the null hypothesis that Beta0 (intercep) = Beta1 (Saves) = Beta2 (Runs_Scored) = 0 = Beta2 (Earned_Run_Average) = 0 there are no linear relationship between these 3 variables with Games Won.
• coef of Saves: 0.41 this means there is a positive relationship between Saves and Games Won and if Saves is held constant, then Games Won is expected to increase by 0.41 for each additional unit of Saves
• coef of Runs_Scored: 0.09 this means there is a positive relationship between Runs Scored and Games Won and if Runs Scored is held constant, then Games Won is expected to increase by 0.09 for each additional unit of Runs Scored
• coef of Earned_Run_Average: -12.68 this means there is a reverse relationship between Earned_Run_Average and Games Won, and if Earned_Run_Average is held constant, then Games Won is expected to decrease by 12.68 for each additional unit of Runs Scored

Conclusion: We will try to add another independent vairable to the model to see if it gets better

Build the model with 4 independents: Saves and Runs_Scored, Earned_Run_Average, Shutout

lm5 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored + Earned_Run_Average + Shutout',data = x_train).fit()
lm5.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.927
Model:	OLS	Adj. R-squared:	0.926
Method:	Least Squares	F-statistic:	1331.
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	5.83e-237
Time:	20:49:57	Log-Likelihood:	-1117.0
No. Observations:	425	AIC:	2244.
Df Residuals:	420	BIC:	2264.
Df Model:	4
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	45.8561	2.444	18.760	0.000	41.051	50.661
Saves	0.4002	0.026	15.142	0.000	0.348	0.452
Runs_Scored	0.0860	0.002	43.942	0.000	0.082	0.090
Earned_Run_Average	-11.3503	0.440	-25.823	0.000	-12.214	-10.486
Shutout	0.3107	0.057	5.496	0.000	0.200	0.422

Omnibus:	0.849	Durbin-Watson:	1.977
Prob(Omnibus):	0.654	Jarque-Bera (JB):	0.754
Skew:	0.102	Prob(JB):	0.686
Kurtosis:	3.030	Cond. No.	1.15e+04

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.15e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

Comment: All the measurement looks good but We will still try to add another independent vairable to the model to see if it gets better

Build the model with 5 independents: Saves and Runs_Scored, Earned_Run_Average, Shutout, Walks

lm6 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored + Earned_Run_Average + Shutout + Walks',data = x_train).fit()
lm6.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.927
Model:	OLS	Adj. R-squared:	0.926
Method:	Least Squares	F-statistic:	1069.
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	6.77e-236
Time:	20:47:14	Log-Likelihood:	-1115.8
No. Observations:	425	AIC:	2244.
Df Residuals:	419	BIC:	2268.
Df Model:	5
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	44.9275	2.512	17.884	0.000	39.989	49.866
Saves	0.4004	0.026	15.178	0.000	0.349	0.452
Runs_Scored	0.0835	0.003	33.043	0.000	0.079	0.088
Earned_Run_Average	-11.2425	0.444	-25.308	0.000	-12.116	-10.369
Shutout	0.3151	0.057	5.577	0.000	0.204	0.426
Walks	0.0042	0.003	1.556	0.120	-0.001	0.010

Omnibus:	1.041	Durbin-Watson:	1.987
Prob(Omnibus):	0.594	Jarque-Bera (JB):	0.987
Skew:	0.118	Prob(JB):	0.611
Kurtosis:	2.999	Cond. No.	1.45e+04

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.45e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

Comment: R-squared and Adj. R-squared do not change, which means adding Shutout does not make the model better. So we will finalize our regression model with 4 variables only: Saves and Runs_Scored, Earned_Run_Average, Shutout

Final Model

lm5 = smf.ols(formula='Games_Won ~ Saves + Runs_Scored + Earned_Run_Average + Shutout',data = x_train).fit()
lm5.summary()

OLS Regression Results

Dep. Variable:	Games_Won	R-squared:	0.927
Model:	OLS	Adj. R-squared:	0.926
Method:	Least Squares	F-statistic:	1331.
Date:	Tue, 19 Dec 2023	Prob (F-statistic):	5.83e-237
Time:	20:47:15	Log-Likelihood:	-1117.0
No. Observations:	425	AIC:	2244.
Df Residuals:	420	BIC:	2264.
Df Model:	4
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	45.8561	2.444	18.760	0.000	41.051	50.661
Saves	0.4002	0.026	15.142	0.000	0.348	0.452
Runs_Scored	0.0860	0.002	43.942	0.000	0.082	0.090
Earned_Run_Average	-11.3503	0.440	-25.823	0.000	-12.214	-10.486
Shutout	0.3107	0.057	5.496	0.000	0.200	0.422

Omnibus:	0.849	Durbin-Watson:	1.977
Prob(Omnibus):	0.654	Jarque-Bera (JB):	0.754
Skew:	0.102	Prob(JB):	0.686
Kurtosis:	3.030	Cond. No.	1.15e+04

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.15e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

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Section 4.2 Evaluation of Regression Model for Period 4

After conducting a train/test split and exploiing the best options for the Linear Regression Model, we selected the following variables for the final model:

• Saves
• Runs_Scored
• Earned_Run_Average
• Shutout

Evaluation

• Both R-squared R-squared Adjusted are 0.92 which means 92.6% variability in Games Won explained by the variability in Saves and Runs_Scored, Earned_Run_Average, and Shutout
• p-value of F-statistic = 2.84e-232 is smaller than 0.05 (at 95% level of confidence) and F-statistic is 1331 which is greater than the F-critical valye. We can reject the null hypothesis that there is no linear relationship between the independent variables (Saves, Runs_Scored, Earned_Run_Average, and Shutout) and Games Won
• p-values of t-tests testing how likely our coefficients are measured through our model by chance. The p-values of 0 for Wealth is saying there is a very little chance the Saves, Runs_Scored, Earned_Run_Average, and Shutout variables have no affect on the dependent variable, Games_Won, and our results are produced by chance (at 95% level of confidence)
• coef of Saves: 0.40 this means there is a positive relationship between Saves and Games Won and if Saves is held constant, then Games Won is expected to increase by 0.40 for each additional unit of Saves
• coef of Runs_Scored: 0.09 this means there is a positive relationship between Runs Scored and Games Won and if Runs Scored is held constant, then Games Won is expected to increase by 0.09 for each additional unit of Runs Scored
• coef of Earned_Run_Average: -11.35 this means there is a reverse relationship between Earned_Run_Average and Games Won, and if Earned_Run_Average is held constant, then Games Won is expected to decrease by 12.68 for each additional unit of Runs Scored
• coef of Shutout: 0.31 this means there is a positibe relationship between Shutout and Games Won, and if Shutout is held constant, then Games Won is expected to increase by 0.31 for each additional unit of Runs Scored

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Section 4 – Linear Regression Models
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Section 5 – Model Validation

Section 5.1 Generating Predictions

x_test.head()

	Year	Games_Won	Earned_Run_Average	Shutout	Saves	Strikeouts_Allowed	Walks	Runs_Scored	Hits	Doubles
2112	1992	92	3.43	14	39	793	511	740	1477	272
2284	1998	88	3.77	16	46	1129	572	706	1425	289
2194	1995	78	3.66	11	37	1060	468	634	1303	191
2512	2006	78	4.41	13	24	948	556	870	1576	351
2234	1996	88	3.98	11	43	1050	495	759	1468	281

x_test.describe()

	Year	Games_Won	Earned_Run_Average	Shutout	Saves	Strikeouts_Allowed	Walks	Runs_Scored	Hits	Doubles
count	183.000000	183.000000	183.000000	183.000000	183.000000	183.000000	183.000000	183.000000	183.000000	183.000000
mean	2000.202186	79.852459	4.274153	8.715847	40.322404	1019.934426	534.584699	739.830601	1436.469945	277.956284
std	6.301718	12.015790	0.551943	4.036389	7.838331	140.752749	71.816786	87.186227	113.773237	36.096151
min	1990.000000	49.000000	3.140000	1.000000	20.000000	602.000000	336.000000	500.000000	966.000000	160.000000
25%	1994.000000	71.000000	3.835000	6.000000	36.000000	931.000000	487.500000	687.500000	1398.000000	260.000000
50%	2001.000000	80.000000	4.230000	9.000000	40.000000	1031.000000	534.000000	740.000000	1445.000000	281.000000
75%	2006.000000	89.000000	4.585000	11.000000	45.000000	1114.000000	578.000000	799.000000	1499.500000	300.500000
max	2010.000000	114.000000	6.020000	20.000000	68.000000	1346.000000	707.000000	993.000000	1644.000000	358.000000

lm5.predict = lm5.predict(x_test)

predict_values=pd.concat([x_test['Year'],x_test['Games_Won'],lm5.predict],axis=1).set_index('Year')
predict_values.columns=['actual_Games_Won','predicted_Games_Won']
predict_values['residual']=predict_values['actual_Games_Won']-predict_values['predicted_Games_Won']
predict_values.head(20)

	actual_Games_Won	predicted_Games_Won	residual
Year
1992	92	90.530145	1.469855
1998	88	87.169064	0.830936
1995	78	77.069830	0.930170
2006	78	84.275542	-6.275542
1996	88	86.590368	1.409632
1998	74	70.343301	3.656699
2002	98	90.921032	7.078968
2006	83	79.504364	3.495636
1998	98	96.105387	1.894613
1993	64	69.714215	-5.714215
2008	92	92.766568	-0.766568
1990	65	67.023082	-2.023082
1999	84	84.364780	-0.364780
1990	70	73.097472	-3.097472
2000	85	86.651801	-1.651801
1994	58	52.849387	5.150613
1995	74	67.247127	6.752873
1998	76	78.137328	-2.137328
2008	84	81.719385	2.280615
1991	83	86.466305	-3.466305

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Section 5 – Model Validation
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Section 5.2. Testing the Error of Predictions - Actual Wins vs. Predicted Wins

rmse=np.sqrt(metrics.mean_squared_error(predict_values['actual_Games_Won'],predict_values['predicted_Games_Won']))

print('RMSE metric for the residuals: %.4f' %rmse)

RMSE metric for the residuals: 3.4821

SI = rmse/predict_values['actual_Games_Won'].mean()*100
print('Scatter Index:', SI)

Scatter Index: 4.360714011847737

sns.regplot(data=predict_values, x='actual_Games_Won', y='predicted_Games_Won', x_estimator=None, x_bins=None, x_ci='ci', scatter=True, fit_reg=True, ci=95, n_boot=1000, units=None, seed=None, order=1, logistic=False, lowess=False, robust=False, logx=False, x_partial=None, y_partial=None, truncate=True, dropna=True, x_jitter=None, y_jitter=None, label=None, color=None, marker='o', scatter_kws=None, line_kws=None, ax=None)

<Axes: xlabel='actual_Games_Won', ylabel='predicted_Games_Won'>

This means that the expected accuracy of the prediction is +/ 3.4821

As suggested in Section 1, the thresholds for RMSE and SI is +/5 adnd 5% respectively, we can assume that expected accuracy of the prediction is acceptable

From the scatterplot, we can see that the residual do not contradict the linear assumption that means it's a good predictor of the Games Won in Period 4

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Section 1 – Objectives of Your Project

Section 5 – Model Validation
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Section 6 – Predictions

df5=data_baseball[(data_baseball['Year']>=2012) & (data_baseball['Year']<=2015)]
df5.head(5)

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
2685	2012	ARI	ARI	3	162	81	81	734	5462	1416	...	39	4301	1432	155	417	1200	90	146.0	0.985	Arizona Diamondbacks
2686	2012	ATL	ATL	2	162	94	68	700	5425	1341	...	47	4336	1310	145	464	1232	86	147.0	0.986	Atlanta Braves
2687	2012	BAL	BAL	2	162	93	69	712	5560	1375	...	55	4449	1433	184	481	1177	106	151.0	0.983	Baltimore Orioles
2688	2012	BOS	BOS	5	162	69	93	734	5604	1459	...	35	4329	1449	190	529	1176	101	159.0	0.983	Boston Red Sox
2689	2012	CHA	CHW	2	162	85	77	748	5518	1409	...	37	4337	1365	186	503	1246	70	154.0	0.988	Chicago White Sox

5 rows × 31 columns

df5_NY=df5[df5['Team']=='NYA']

df5_NY

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
2702	2012	NYA	NYY	1	162	95	67	804	5524	1462	...	51	4336	1401	190	431	1318	75	135.0	0.987	New York Yankees
2732	2013	NYA	NYY	4	162	85	77	650	5449	1321	...	49	4342	1452	171	437	1233	69	139.0	0.988	New York Yankees
2762	2014	NYA	NYY	2	162	84	78	633	5497	1349	...	48	4359	1392	164	398	1370	92	107.0	0.984	New York Yankees
2781	2015	NYA	NYY	2	162	87	75	764	5567	1397	...	48	4373	1416	182	474	1370	93	135.0	0.985	New York Yankees

4 rows × 31 columns

df5_TO=df5[df5['Team']=='TOR']
df5_TO

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
2713	2012	TOR	TOR	4	162	73	89	716	5487	1346	...	29	4331	1439	204	574	1142	101	167.0	0.984	Toronto Blue Jays
2743	2013	TOR	TOR	5	162	74	88	712	5537	1398	...	39	4356	1451	195	500	1208	111	145.0	0.982	Toronto Blue Jays
2773	2014	TOR	TOR	3	162	83	79	723	5549	1435	...	45	4329	1400	151	490	1199	87	130.0	0.985	Toronto Blue Jays
2780	2015	TOR	TOR	1	162	93	69	891	5509	1480	...	34	4323	1353	173	397	1117	88	145.0	0.985	Toronto Blue Jays

4 rows × 31 columns

data_baseball_5=pd.concat([df5_NY,df5_TO],axis=0)
data_baseball_5.reset_index(drop=True)

	Year	Team	Franchise	Final_Standing	Games_Played	Games_Won	Games_Lost	Runs_Scored	At_Bats	Hits	...	Saves	Infield_Put_Outs	Hits_Allowed	Home_Run_Allowed	Walks_Allowed	Strikeouts_Allowed	Errors	Double_Plays	Fielding_Percentage	Team_Name
0	2012	NYA	NYY	1	162	95	67	804	5524	1462	...	51	4336	1401	190	431	1318	75	135.0	0.987	New York Yankees
1	2013	NYA	NYY	4	162	85	77	650	5449	1321	...	49	4342	1452	171	437	1233	69	139.0	0.988	New York Yankees
2	2014	NYA	NYY	2	162	84	78	633	5497	1349	...	48	4359	1392	164	398	1370	92	107.0	0.984	New York Yankees
3	2015	NYA	NYY	2	162	87	75	764	5567	1397	...	48	4373	1416	182	474	1370	93	135.0	0.985	New York Yankees
4	2012	TOR	TOR	4	162	73	89	716	5487	1346	...	29	4331	1439	204	574	1142	101	167.0	0.984	Toronto Blue Jays
5	2013	TOR	TOR	5	162	74	88	712	5537	1398	...	39	4356	1451	195	500	1208	111	145.0	0.982	Toronto Blue Jays
6	2014	TOR	TOR	3	162	83	79	723	5549	1435	...	45	4329	1400	151	490	1199	87	130.0	0.985	Toronto Blue Jays
7	2015	TOR	TOR	1	162	93	69	891	5509	1480	...	34	4323	1353	173	397	1117	88	145.0	0.985	Toronto Blue Jays

8 rows × 31 columns

lm5.predict2 = lm5.predict(data_baseball_5)
predict_values2=pd.concat([data_baseball_5['Year'],data_baseball_5['Games_Won'],lm5.predict2],axis=1).set_index('Year')
predict_values2.columns=['actual_Games_Won','predicted_Games_Won']
predict_values2['residual']=predict_values2['actual_Games_Won']-predict_values2['predicted_Games_Won']
predict_values2.head(20)

	actual_Games_Won	predicted_Games_Won	residual
Year
2012	95	94.629938	0.370062
2013	85	79.759212	5.240788
2014	84	80.053377	3.946623
2015	87	86.279008	0.720992
2012	73	69.798379	3.201621
2013	74	77.882529	-3.882529
2014	83	85.620568	-2.620568
2015	93	96.075066	-3.075066

rmse=np.sqrt(metrics.mean_squared_error(predict_values2['actual_Games_Won'],predict_values2['predicted_Games_Won']))
print(rmse)

3.2662343220952215

sns.regplot(data=predict_values2, x='actual_Games_Won', y='predicted_Games_Won', x_estimator=None, x_bins=None, x_ci='ci', scatter=True, fit_reg=True, ci=95, n_boot=1000, units=None, seed=None, order=1, logistic=False, lowess=False, robust=False, logx=False, x_partial=None, y_partial=None, truncate=True, dropna=True, x_jitter=None, y_jitter=None, label=None, color=None, marker='o', scatter_kws=None, line_kws=None, ax=None)

<Axes: xlabel='actual_Games_Won', ylabel='predicted_Games_Won'>

As suggested in Section 1, the thresholds for RMSE and SI is +/5 adnd 5% respectively, we can assume that expected accuracy of the prediction is acceptable

From the scatterplot, we can see that the residual do not contradict the linear assumption that means it's a good predictor of the Games Won for New York Yankees and Toronto Blue Jays from 2012 to 2015

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Section 6 – Predictions
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Section 7 - Conclusions

Data Cleaning process: we detected variables that have missing data and used appropriate method to either remove it from the dataset or use it for the period that it has full data. This elimates the chance that we might remove important variables that can possible have a strong correlation with Games Won in a certain period

After completing the data analysis process, we are able to determine the style of play for each period from 4 periods from 1871 to 2010. Also, with 95% level of confidence, we also built a model that can forecast future results by making predictions based on previous data (period 1990 to 2010) with accuracy of the prediction is +/ over 3

Throughout the project, we have used correlation calculation to determine the correlation relationship between dependent variable and independent variables, and determine the style of play for each period. QQ plots, Scatter Plots, Scatter Matrix, Box Plots, and Histogram are also used to check the normality, linear relationships, Outliers, etc. This meets the analytical objectives that we set in Section 1

Recommendations for next steps

• Overall, the regression model has quite good measurements (R-squared, Adjusted R-square, F-statistic, RMSE); however, we could have eliminated the numbers of independent variables to avoid Curse of dimensionality. We could calculate RMSE with the model that only has 2 variables or 1 variable only to estimate the prediction ability of the model(s) and compare with the model that we have in this project. Even though RMSE is not too bad, there is a chance that we can get a better RMSE
• Multicollinearity: need an improvement on detecting the multicollinearity (such as VIF) so this process could be less time consuming. We could have been also tried to elimate any independent variables that have over 0.5 correlation with other independent variables to compare the results
• Even though determining the style of play for each period might be helpful, we could also dig deeper into the data and find out which style of play of each team in each period of time. This could be very beneficial for the coaches to plan game strategy for the team
• We could also use the Team Perfomance Varibles (Games Played, Games Lost, etc) and Offensive, Defensive measurements to analyze the on-field perfomance of each team through the years (improved or got worse)
• Applying the same teachnique for new dataset to predict future results

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Section 7 - Conclusions
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The end